{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib.pyplot as plt \n",
    "import seaborn as sns\n",
    "from ERANataf import ERANataf\n",
    "from ERADist import ERADist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Updating \n",
    "    Conjugate prior case\n",
    "    L(xi,theta) : Xi ~ Normal(theta,sigma_X = 1)\n",
    "    L((x1,x2,...xN),theta) = L(x1,theta)*L(x2,theta)*...*L(xN,theta)\n",
    "    Prior ~ normal (mu_theta_prior. sigma_theta_prior)\n",
    "    Posterior: ~ normal (mu_theta_posterior, sigma_theta_posterior)\n",
    "    \n",
    "    # Analytical solution:\n",
    "    mu_theta_posterior = (mu_theta_prior/sigma_theta_prior^2+N*x_bar/sigma_X^2)/(1/sigma_theta_prior^2+N/sigma_X^2)\n",
    "    sigma_theta_posterior = (1/sigma_theta_prior^2+N/sigma_X^2)^(-1/2)\n",
    "    # Numerical\n",
    "    posterior_PDF is proportional to the (Prior_PDF*Likelihood)\n",
    "    first calculate target_dist = Prior_PDF*Likelihood\n",
    "    then either do the numerical integration\n",
    "    or do the sample-based approach\n",
    "        # Cross Entropy Bayesian Updating\n",
    "        1. Original scale self version/ function call\n",
    "        2. Log scale self version/ function call\n",
    "        \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.39038036789285785"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This is an example where prior p(mu) ~ N(0,1),\n",
    "mu_theta_prior, sigma_theta_prior = -5, 1\n",
    "prior = lambda theta: sp.stats.norm.pdf(theta,loc = mu_theta_prior, scale = sigma_theta_prior)\n",
    "log_prior = lambda theta: sp.stats.norm.logpdf(theta,loc=mu_theta_prior,scale = sigma_theta_prior)\n",
    "# Likelihood functions p(D|mu) ~ normal\n",
    "data = np.random.randn(10)\n",
    "np.mean(data)#data.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Likelihood function\n",
    "def Likelihood(theta):\n",
    "    total_likelihood = 1\n",
    "    sigma_X  = 1\n",
    "    for i in range(data.size):\n",
    "        total_likelihood = total_likelihood*sp.stats.norm.pdf(data[i],loc = theta, scale = sigma_X)\n",
    "    return total_likelihood\n",
    "def log_Likelihood(theta):\n",
    "    total_likelihood = 0\n",
    "    sigma_X  = 1\n",
    "    for i in range(data.size):\n",
    "        total_likelihood = total_likelihood+sp.stats.norm.logpdf(data[i],loc = theta, scale = sigma_X)\n",
    "    return total_likelihood\n",
    "# Posterior distribution\n",
    "def target_dist(theta):\n",
    "    return prior(theta)*Likelihood(theta)\n",
    "\n",
    "def log_target_dist(theta):\n",
    "    return log_prior(theta)+log_Likelihood(theta)\n",
    "\n",
    "def posterior_analytical(mu_theta_prior,sigma_theta_prior,data):\n",
    "    n = data.size\n",
    "    x_bar = np.mean(data)\n",
    "    sigma_X = 1\n",
    "    mu_theta_posterior = (mu_theta_prior/sigma_theta_prior**2+n*x_bar/sigma_X**2)/(1/sigma_theta_prior**2+n/sigma_X**2)\n",
    "    sigma_theta_posterior = (1/sigma_theta_prior**2+n/sigma_X**2)**(-1/2)\n",
    "    return sp.stats.norm.pdf(theta,loc = mu_theta_posterior, scale = sigma_theta_posterior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.137341001451469e-13, 1.6177220889355334e-14)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "constant = sp.integrate.quad(target_dist,-np.inf,np.inf)\n",
    "constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00000000e+000, 0.00000000e+000, 0.00000000e+000, 0.00000000e+000,\n",
       "       0.00000000e+000, 0.00000000e+000, 0.00000000e+000, 0.00000000e+000,\n",
       "       0.00000000e+000, 2.04974369e-284, 9.92293632e-235, 8.02308789e-190,\n",
       "       1.08343683e-149, 2.44357874e-114, 9.20470302e-084, 5.79100477e-058,\n",
       "       6.08497452e-037, 1.06788455e-020, 3.13004472e-009, 1.53227770e-002,\n",
       "       1.25280973e+000, 1.71077720e-003, 3.90177741e-011, 1.48625122e-023,\n",
       "       9.45545990e-041, 1.00469396e-062, 1.78297651e-089, 5.28467339e-121,\n",
       "       2.61608217e-157, 2.16294417e-198, 2.98675733e-244, 6.88835094e-295,\n",
       "       0.00000000e+000, 0.00000000e+000, 0.00000000e+000, 0.00000000e+000,\n",
       "       0.00000000e+000, 0.00000000e+000, 0.00000000e+000, 0.00000000e+000])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = np.arange(-20,20)\n",
    "posterior_analytical(mu_theta_prior,sigma_theta_prior,data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24aaf1b6b08>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta = np.arange(-20,20)\n",
    "plt.plot(theta,posterior_analytical(mu_theta_prior,sigma_theta_prior,data),'-o',label='posterior_analytical')\n",
    "plt.plot(theta,target_dist(theta)/constant[0],'-x',label='posterior_numerical')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24aaf4fd048>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta = np.arange(-20,20)\n",
    "plt.plot(theta,prior(theta),'-+',label='prior')\n",
    "plt.plot(theta,Likelihood(theta),'-*',label='Likelihood')\n",
    "plt.plot(theta,target_dist(theta)/constant[0],'-o',label='posterior')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cross Entropy Method for Bayesian Updating"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "CE-based IS stage: \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Self version\n",
    "# Parameter definition\n",
    "# Target distribution\n",
    "#  Parameter definition\n",
    "# This is an example where prior p(mu) ~ N(0,1),\n",
    "mu_theta_prior, sigma_theta_prior = -10, 1\n",
    "prior = lambda theta: sp.stats.norm.pdf(theta,loc = mu_theta_prior, scale = sigma_theta_prior)\n",
    "log_prior = lambda theta: sp.stats.norm.logpdf(theta,loc=mu_theta_prior,scale = sigma_theta_prior)\n",
    "theta_prior = ERADist(\"Normal\",\"MOM\",[mu_theta_prior, sigma_theta_prior])\n",
    "# Likelihood functions p(D|mu) ~ normal\n",
    "data = np.random.randn(10)\n",
    "# Likelihood function\n",
    "def Likelihood(theta):\n",
    "    total_likelihood = 1\n",
    "    sigma_X  = 1\n",
    "    for i in range(data.size):\n",
    "        total_likelihood = total_likelihood*sp.stats.norm.pdf(data[i],loc = theta, scale = sigma_X)\n",
    "    return total_likelihood\n",
    "def log_Likelihood(theta):\n",
    "    total_likelihood = 0\n",
    "    sigma_X  = 1\n",
    "    for i in range(data.size):\n",
    "        total_likelihood = total_likelihood+sp.stats.norm.logpdf(data[i],loc = theta, scale = sigma_X)\n",
    "    return total_likelihood\n",
    "def target_dist_t(theta,beta_t):\n",
    "    return prior(theta)*(Likelihood(theta))**beta_t\n",
    "def log_target_dist_t(theta,beta_t):\n",
    "    return log_prior(theta)+beta_t*log_Likelihood(theta)\n",
    "\n",
    "# # Posterior distribution\n",
    "# def target_dist(theta):\n",
    "#     return prior(theta)*Likelihood(theta)\n",
    "\n",
    "# def log_target_dist(theta):\n",
    "#     return log_prior(theta)+log_Likelihood(theta)\n",
    "N = 1000\n",
    "dim = 1\n",
    "max_it = 50\n",
    "CV_target = 0.5\n",
    "print('\\nCE-based IS stage: ')\n",
    "# transform the prior,likelihood and posterior distribution to the normal space\n",
    "# Prior transformation\n",
    "# Here X~ N(mu_X,sigma_X)\n",
    "# U = (X-mu_X)/sigma_X; X = mu_X + sigma_X*U\n",
    "x2u_prior = lambda x: (x-mu_theta_prior)/sigma_theta_prior\n",
    "u2x_prior = lambda u: mu_theta_prior+sigma_theta_prior*u\n",
    "# Likelihood in transformed space\n",
    "L_transformed = lambda u: Likelihood(u2x_prior(u))\n",
    "N_tot = 0 # Total number of samples\n",
    "# Definition of parameters of random variables\n",
    "mu_init = np.zeros(dim)\n",
    "si_init = np.identity(dim)\n",
    "beta_t = np.zeros(max_it)\n",
    "samplesU = list()\n",
    "# CE procedure (multinormal parametric family)\n",
    "mu_U = mu_init\n",
    "si_U = si_init\n",
    "# Iteration\n",
    "for t in range(max_it):\n",
    "    # Generate samples and save them\n",
    "    U = sp.stats.multivariate_normal.rvs(mean= mu_U,cov=si_U, size =N).reshape(-1,dim)\n",
    "    samplesU.append(U.T)\n",
    "    # Count generated samples\n",
    "    N_tot += N\n",
    "    # Evaluate the likelihood function\n",
    "    Leval = Likelihood(u2x_prior(U)) \n",
    "    # Initalize beta, beta increases from 0 to 1\n",
    "    if t == 0:\n",
    "        beta_t[t] = 0\n",
    "    else:\n",
    "        beta_t[t] = beta_new\n",
    "    # calculating h for the likelihood ratio\n",
    "    h = sp.stats.multivariate_normal.pdf(U,mu_U,si_U)\n",
    "    phi = sp.stats.multivariate_normal.pdf(U,mean=np.zeros(dim),cov=np.identity(dim))\n",
    "    # Likelihood ratio for the original CE weight\n",
    "    W = phi/h\n",
    "\n",
    "#    if beta_t[t] >= 1-1e-6:\n",
    "#        break\n",
    "#     # Solve the optimisation problem\n",
    "    Wt_fun = lambda beta: W*np.power(Leval,beta)[:,0]\n",
    "    CV_Wt_fun = lambda beta: np.std(Wt_fun(beta))/np.mean(Wt_fun(beta))\n",
    "#    fmin = lambda beta: abs(CV_Wt_fun(beta)-CV_target)\n",
    "    ESS_target = N/(1+CV_target**2)\n",
    "    ESS_observed = lambda beta: N/(1+(CV_Wt_fun(beta))**2)\n",
    "    fmin = lambda beta: abs(ESS_target-ESS_observed(beta))\n",
    "    beta_new = sp.optimize.fminbound(fmin,beta_t[t],1)\n",
    "    # Update W_t\n",
    "    W_t = Wt_fun(beta_new)\n",
    "    delta_Wt = np.std(W_t)/np.mean(W_t)\n",
    "    if beta_new >= 1-1e-6:\n",
    "        break\n",
    "    # Parameter update: closed form\n",
    "    mu_U = W_t@U/sum(W_t)\n",
    "    Xtmp = U-mu_U\n",
    "    Xo = Xtmp *np.tile(np.sqrt(W_t),(dim,1)).T\n",
    "    Si_U = np.matmul(Xo.T,Xo)/np.sum(W_t)+1e-6*np.identity(dim)\n",
    "#total levels\n",
    "lv = t\n",
    "# Calculation of the integral of the posterior = 1\n",
    "Integral = sum(W_t)/N\n",
    "# Calculation of the integral of the target_dist\n",
    "#Integral_target = \n",
    "# Transform the samples to the physical/ original space\n",
    "samplesX = list()\n",
    "for i in range(lv):\n",
    "    samplesX.append(u2x_prior(samplesU[i]))\n",
    "# Plot samples \n",
    "if dim == 1:\n",
    "    nnp = 200\n",
    "    xx = np.linspace(-6,6,nnp)\n",
    "    sns.distplot(samplesU[0],label='beta=0')\n",
    "    for sample in samplesU[1:-1]:\n",
    "        sns.distplot(sample)\n",
    "        #plt.plot(*sample,\".\",markersize=2)\n",
    "    sns.distplot(samplesU[-1],label='beta=1')\n",
    "    plt.xlabel('u')\n",
    "    plt.ylabel('target_dist')\n",
    "    plt.title('Intermediate target distribution in tranformed space')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "if dim == 1:\n",
    "    nnp = 200\n",
    "    xx = np.linspace(-6,6,nnp)\n",
    "    sns.distplot(samplesX[0],label='beta=0')\n",
    "    for sample in samplesX[1:-1]:\n",
    "        sns.distplot(sample)\n",
    "        #plt.plot(*sample,\".\",markersize=2)\n",
    "    sns.distplot(samplesX[-1],label='beta=1')\n",
    "    plt.title('Intermediate target distribution in physical space')\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.00452495, 0.01003077, 0.01693392, 0.02426385,\n",
       "       0.03233231, 0.041544  , 0.04996602, 0.0610602 , 0.07141632,\n",
       "       0.08214764, 0.09424118, 0.10639982, 0.11884143, 0.13107767,\n",
       "       0.13824237, 0.14300847, 0.14830146, 0.14830634, 0.15223003,\n",
       "       0.15401067, 0.15445383, 0.15759131, 0.1575961 , 0.15760089,\n",
       "       0.15760568, 0.1623605 , 0.16236524, 0.16236999, 0.16237473,\n",
       "       0.16237947, 0.16238422, 0.16238896, 0.1623937 , 0.16239844,\n",
       "       0.16240319, 0.16240793, 0.16241267, 0.16241741, 0.16242216,\n",
       "       0.1624269 , 0.16243164, 0.16243639, 0.16244113, 0.16244587,\n",
       "       0.16245061, 0.16245535, 0.1669438 , 0.1669485 , 0.1669532 ])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta_t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "CE-based IS stage: \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Self version\n",
    "# Parameter definition\n",
    "# Target distribution\n",
    "#  Parameter definition\n",
    "# This is an example where prior p(mu) ~ N(0,1),\n",
    "mu_theta_prior, sigma_theta_prior = -10, 1\n",
    "prior = lambda theta: sp.stats.norm.pdf(theta,loc = mu_theta_prior, scale = sigma_theta_prior)\n",
    "log_prior = lambda theta: sp.stats.norm.logpdf(theta,loc=mu_theta_prior,scale = sigma_theta_prior)\n",
    "theta_prior = ERADist(\"Normal\",\"MOM\",[mu_theta_prior, sigma_theta_prior])\n",
    "# Likelihood functions p(D|mu) ~ normal\n",
    "data = np.random.randn(10)\n",
    "# Likelihood function\n",
    "def Likelihood(theta):\n",
    "    total_likelihood = 1\n",
    "    sigma_X  = 1\n",
    "    for i in range(data.size):\n",
    "        total_likelihood = total_likelihood*sp.stats.norm.pdf(data[i],loc = theta, scale = sigma_X)\n",
    "    return total_likelihood\n",
    "def log_Likelihood(theta):\n",
    "    total_likelihood = 0\n",
    "    sigma_X  = 1\n",
    "    for i in range(data.size):\n",
    "        total_likelihood = total_likelihood+sp.stats.norm.logpdf(data[i],loc = theta, scale = sigma_X)\n",
    "    return total_likelihood\n",
    "def target_dist_t(theta,beta_t):\n",
    "    return prior(theta)*(Likelihood(theta))**beta_t\n",
    "def log_target_dist_t(theta,beta_t):\n",
    "    return log_prior(theta)+beta_t*log_Likelihood(theta)\n",
    "\n",
    "# # Posterior distribution\n",
    "# def target_dist(theta):\n",
    "#     return prior(theta)*Likelihood(theta)\n",
    "\n",
    "# def log_target_dist(theta):\n",
    "#     return log_prior(theta)+log_Likelihood(theta)\n",
    "N = 1000\n",
    "dim = 1\n",
    "max_it = 100\n",
    "CV_target = 1.5\n",
    "print('\\nCE-based IS stage: ')\n",
    "# transform the prior,likelihood and posterior distribution to the normal space\n",
    "# Prior transformation\n",
    "# Here X~ N(mu_X,sigma_X)\n",
    "# U = (X-mu_X)/sigma_X; X = mu_X + sigma_X*U\n",
    "x2u_prior = lambda x: (x-mu_theta_prior)/sigma_theta_prior\n",
    "u2x_prior = lambda u: mu_theta_prior+sigma_theta_prior*u\n",
    "# Likelihood in transformed space\n",
    "L_transformed = lambda u: Likelihood(u2x_prior(u))\n",
    "N_tot = 0 # Total number of samples\n",
    "# Definition of parameters of random variables\n",
    "mu_init = np.zeros(dim)\n",
    "si_init = np.identity(dim)\n",
    "beta_t = np.zeros(max_it)\n",
    "samplesU = list()\n",
    "# CE procedure (multinormal parametric family)\n",
    "mu_U = mu_init\n",
    "si_U = si_init\n",
    "# Iteration\n",
    "for t in range(max_it):\n",
    "    # Generate samples and save them\n",
    "    U = sp.stats.multivariate_normal.rvs(mean= mu_U,cov=si_U, size =N).reshape(-1,dim)\n",
    "    samplesU.append(U.T)\n",
    "    # Count generated samples\n",
    "    N_tot += N\n",
    "    # Evaluate the likelihood function\n",
    "    Leval = Likelihood(u2x_prior(U)) \n",
    "    # Initalize beta, beta increases from 0 to 1\n",
    "    if t == 0:\n",
    "        beta_t[t] = 0\n",
    "    else:\n",
    "        beta_t[t] = beta_new\n",
    "    # calculating h for the likelihood ratio\n",
    "    h = sp.stats.multivariate_normal.pdf(U,mu_U,si_U)\n",
    "    phi = sp.stats.multivariate_normal.pdf(U,mean=np.zeros(dim),cov=np.identity(dim))\n",
    "    # Likelihood ratio for the original CE weight\n",
    "    W = phi/h\n",
    "    # improved CE Likelihood weight W_t = W*l**Beta_t\n",
    "    # W_t = W.reshape(N,-1)*Leval**beta_t[t]\n",
    "#     # CV of W_t\n",
    "#     delta_Wt = np.std(W_t)/np.mean(W_t)\n",
    "#     if delta_Wt <= CV_target:\n",
    "#         break\n",
    "    if beta_t[t] >= 1-1e-6:\n",
    "        break\n",
    "#     # Solve the optimisation problem\n",
    "    Wt_fun = lambda beta: W*np.power(Leval,beta)[:,0]\n",
    "    CV_Wt_fun = lambda beta: np.std(Wt_fun(beta))/np.mean(Wt_fun(beta))\n",
    "#    fmin = lambda beta: abs(CV_Wt_fun(beta)-CV_target)\n",
    "    ESS_target = N/(1+CV_target**2)\n",
    "    ESS_observed = lambda beta: N/(1+(CV_Wt_fun(beta))**2)\n",
    "    fmin = lambda beta: abs(ESS_target-ESS_observed(beta))\n",
    "    beta_new = sp.optimize.fminbound(fmin,beta_t[t],1)\n",
    "    # Update W_t\n",
    "    W_t = Wt_fun(beta_new)\n",
    "    # Parameter update: closed form\n",
    "    mu_U = W_t@U/sum(W_t)\n",
    "    Xtmp = U-mu_U\n",
    "    Xo = Xtmp *np.tile(np.sqrt(W_t),(dim,1)).T\n",
    "    Si_U = np.matmul(Xo.T,Xo)/np.sum(W_t)+1e-6*np.identity(dim)\n",
    "#total levels\n",
    "lv = t\n",
    "# Calculation of the integral of the posterior = 1\n",
    "Integral = sum(W_t)/N\n",
    "# Calculation of the integral of the target_dist\n",
    "#Integral_target = \n",
    "# Transform the samples to the physical/ original space\n",
    "samplesX = list()\n",
    "for i in range(lv):\n",
    "    samplesX.append(u2x_prior(samplesU[i]))\n",
    "# Plot samples \n",
    "if dim == 1:\n",
    "    nnp = 200\n",
    "    xx = np.linspace(-6,6,nnp)\n",
    "    sns.distplot(samplesU[0],label='beta=0')\n",
    "    for sample in samplesU[1:-1]:\n",
    "        sns.distplot(sample)\n",
    "        #plt.plot(*sample,\".\",markersize=2)\n",
    "    sns.distplot(samplesU[-1],label='beta=1')\n",
    "    plt.xlabel('u')\n",
    "    plt.ylabel('target_dist')\n",
    "    plt.title('Intermediate target distribution in tranformed space')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "if dim == 1:\n",
    "    nnp = 200\n",
    "    xx = np.linspace(-6,6,nnp)\n",
    "    sns.distplot(samplesX[0],label='beta=0')\n",
    "    for sample in samplesX[1:-1]:\n",
    "        sns.distplot(sample)\n",
    "        #plt.plot(*sample,\".\",markersize=2)\n",
    "    sns.distplot(samplesX[-1],label='beta=1')\n",
    "    plt.title('Intermediate target distribution in physical space')\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['a', 'b', 'c', 'd', 'e']"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = list(['a','b','c','d','e'])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a\n",
      "b\n",
      "c\n",
      "d\n",
      "e\n"
     ]
    }
   ],
   "source": [
    "for i in a:\n",
    "    print(i) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b\n",
      "c\n",
      "d\n"
     ]
    }
   ],
   "source": [
    "for i in a[1:-1]:\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "if dim == 1:\n",
    "    nnp = 200\n",
    "    xx = np.linspace(-6,6,nnp)\n",
    "    sns.distplot(samplesX[0],label='beta = 0')\n",
    "    for sample in samplesX:\n",
    "        #sns.distplot(sample,label='Intermediate Target dist')\n",
    "        sns.distplot(sample)\n",
    "        #plt.plot(*sample,\".\",markersize=2)\n",
    "    sns.distplot(samplesX[-1],label='beta = 1')\n",
    "    plt.plot(xx,Likelihood(xx),'+',label='Likelihood')\n",
    "    \n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#  CEBU function call\n",
    "# Parameter definition\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if dim == 1:\n",
    "    nnp = 200\n",
    "    xx = np.linspace(-6,6,nnp)\n",
    "    plt.hist(samplesX[0],label='/beta = 0')\n",
    "    for sample in samplesX:\n",
    "        #sns.distplot(sample,label='Intermediate Target dist')\n",
    "        plt.hist(sample)\n",
    "        #plt.plot(*sample,\".\",markersize=2)\n",
    "    plt.hist(samplesX[-1],label='/beta = 1')\n",
    "    plt.plot(xx,Likelihood(xx),'+',label='Likelihood')\n",
    "    \n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if dim == 1:\n",
    "    nnp = 200\n",
    "    xx = np.linspace(-6,6,nnp)\n",
    "    sns.distplot(samplesX[0],label='/beta = 0')\n",
    "    for sample in samplesX:\n",
    "        #sns.distplot(sample,label='Intermediate Target dist')\n",
    "        sns.distplot(sample)\n",
    "        #plt.plot(*sample,\".\",markersize=2)\n",
    "    sns.distplot(samplesX[-1],label='/beta = 1')\n",
    "    plt.plot(xx,Likelihood(xx),'+',label='Likelihood')\n",
    "    \n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.01221375, 0.02858108, 0.04972899, 0.08035243,\n",
       "       0.12836407, 0.20670553, 0.3451137 , 0.65164619, 0.99999456,\n",
       "       0.99999664, 0.99999792, 0.99999872, 0.99999921, 0.99999951,\n",
       "       0.9999997 , 0.99999981, 0.99999988, 0.99999993, 0.99999996,\n",
       "       0.99999997, 0.99999998, 0.99999999, 0.99999999, 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta_t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "419.30300933791153"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ESS_observed(beta_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Self version log scale\n",
    "# Parameter definition\n",
    "# Target distribution\n",
    "#  Parameter definition\n",
    "# This is an example where prior p(mu) ~ N(0,1),\n",
    "mu_theta_prior, sigma_theta_prior = -10, 1\n",
    "prior = lambda theta: sp.stats.norm.pdf(theta,loc = mu_theta_prior, scale = sigma_theta_prior)\n",
    "log_prior = lambda theta: sp.stats.norm.logpdf(theta,loc=mu_theta_prior,scale = sigma_theta_prior)\n",
    "theta_prior = ERADist(\"Normal\",\"MOM\",[mu_theta_prior, sigma_theta_prior])\n",
    "# Likelihood functions p(D|mu) ~ normal\n",
    "data = np.random.randn(10)\n",
    "# Likelihood function\n",
    "def Likelihood(theta):\n",
    "    total_likelihood = 1\n",
    "    sigma_X  = 1\n",
    "    for i in range(data.size):\n",
    "        total_likelihood = total_likelihood*sp.stats.norm.pdf(data[i],loc = theta, scale = sigma_X)\n",
    "    return total_likelihood\n",
    "def log_Likelihood(theta):\n",
    "    total_likelihood = 0\n",
    "    sigma_X  = 1\n",
    "    for i in range(data.size):\n",
    "        total_likelihood = total_likelihood+sp.stats.norm.logpdf(data[i],loc = theta, scale = sigma_X)\n",
    "    return total_likelihood\n",
    "def target_dist_t(theta,beta_t):\n",
    "    return prior(theta)*(Likelihood(theta))**beta_t\n",
    "def log_target_dist_t(theta,beta_t):\n",
    "    return log_prior(theta)+beta_t*log_Likelihood(theta)\n",
    "\n",
    "# # Posterior distribution\n",
    "# def target_dist(theta):\n",
    "#     return prior(theta)*Likelihood(theta)\n",
    "\n",
    "# def log_target_dist(theta):\n",
    "#     return log_prior(theta)+log_Likelihood(theta)\n",
    "N = 1000\n",
    "dim = 1\n",
    "max_it = 100\n",
    "CV_target = 1.5\n",
    "print('\\nCE-based IS stage: ')\n",
    "# transform the prior,likelihood and posterior distribution to the normal space\n",
    "# Prior transformation\n",
    "# Here X~ N(mu_X,sigma_X)\n",
    "# U = (X-mu_X)/sigma_X; X = mu_X + sigma_X*U\n",
    "x2u_prior = lambda x: (x-mu_theta_prior)/sigma_theta_prior\n",
    "u2x_prior = lambda u: mu_theta_prior+sigma_theta_prior*u\n",
    "# Likelihood in transformed space\n",
    "L_transformed = lambda u: Likelihood(u2x_prior(u))\n",
    "N_tot = 0 # Total number of samples\n",
    "# Definition of parameters of random variables\n",
    "mu_init = np.zeros(dim)\n",
    "si_init = np.identity(dim)\n",
    "beta_t = np.zeros(max_it)\n",
    "samplesU = list()\n",
    "# CE procedure (multinormal parametric family)\n",
    "mu_U = mu_init\n",
    "si_U = si_init\n",
    "# Iteration\n",
    "for t in range(max_it):\n",
    "    # Generate samples and save them\n",
    "    U = sp.stats.multivariate_normal.rvs(mean= mu_U,cov=si_U, size =N).reshape(-1,dim)\n",
    "    samplesU.append(U.T)\n",
    "    # Count generated samples\n",
    "    N_tot += N\n",
    "    # Evaluate the likelihood function\n",
    "    Leval = Likelihood(u2x_prior(U)) \n",
    "    # Initalize beta, beta increases from 0 to 1\n",
    "    if t == 0:\n",
    "        beta_t[t] = 0\n",
    "    else:\n",
    "        beta_t[t] = beta_new\n",
    "    # calculating h for the likelihood ratio\n",
    "    h = sp.stats.multivariate_normal.pdf(U,mu_U,si_U)\n",
    "    phi = sp.stats.multivariate_normal.pdf(U,mean=np.zeros(dim),cov=np.identity(dim))\n",
    "    # Likelihood ratio for the original CE weight\n",
    "    W = phi/h\n",
    "    # improved CE Likelihood weight W_t = W*l**Beta_t\n",
    "    # W_t = W.reshape(N,-1)*Leval**beta_t[t]\n",
    "#     # CV of W_t\n",
    "#     delta_Wt = np.std(W_t)/np.mean(W_t)\n",
    "#     if delta_Wt <= CV_target:\n",
    "#         break\n",
    "    if beta_t[t] >= 1-1e-6:\n",
    "        break\n",
    "#     # Solve the optimisation problem\n",
    "    Wt_fun = lambda beta: W*np.power(Leval,beta)[:,0]\n",
    "    CV_Wt_fun = lambda beta: np.std(Wt_fun(beta))/np.mean(Wt_fun(beta))\n",
    "#    fmin = lambda beta: abs(CV_Wt_fun(beta)-CV_target)\n",
    "    ESS_target = N/(1+CV_target**2)\n",
    "    ESS_observed = lambda beta: N/(1+(CV_Wt_fun(beta))**2)\n",
    "    fmin = lambda beta: abs(ESS_target-ESS_observed(beta))\n",
    "    beta_new = sp.optimize.fminbound(fmin,beta_t[t],1)\n",
    "    # Update W_t\n",
    "    W_t = Wt_fun(beta_new)\n",
    "    # Parameter update: closed form\n",
    "    mu_U = W_t@U/sum(W_t)\n",
    "    Xtmp = U-mu_U\n",
    "    Xo = Xtmp *np.tile(np.sqrt(W_t),(dim,1)).T\n",
    "    Si_U = np.matmul(Xo.T,Xo)/np.sum(W_t)+1e-6*np.identity(dim)\n",
    "#total levels\n",
    "lv = t\n",
    "# Calculation of the integral of the posterior = 1\n",
    "Integral = sum(W_t)/N\n",
    "# Calculation of the integral of the target_dist\n",
    "#Integral_target = \n",
    "# Transform the samples to the physical/ original space\n",
    "samplesX = list()\n",
    "for i in range(lv):\n",
    "    samplesX.append(u2x_prior(samplesU[i]))\n",
    "# Plot samples \n",
    "if dim == 1:\n",
    "    nnp = 200\n",
    "    xx = np.linspace(-6,6,nnp)\n",
    "    for sample in samplesU:\n",
    "        sns.distplot(sample)\n",
    "        #plt.plot(*sample,\".\",markersize=2)\n",
    "    plt.show()\n",
    "if dim == 1:\n",
    "    nnp = 200\n",
    "    xx = np.linspace(-6,6,nnp)\n",
    "    for sample in samplesX:\n",
    "        sns.distplot(sample)\n",
    "        #plt.plot(*sample,\".\",markersize=2)\n",
    "    plt.show()    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1,)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu_U.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 1)"
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     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "si_U.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "W_t = Wt_fun(beta_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "0.014582842363196432"
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     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "beta_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000,)"
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     },
     "execution_count": 45,
     "metadata": {},
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   ],
   "source": [
    "W_t[:,0].shape"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {
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       "       [2.07485997e-095],\n",
       "       [4.77239397e-049],\n",
       "       [1.80967098e-102]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Leval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 1000)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(W*Leval).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 1)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(Leval*Leval).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 1)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V=W.reshape(N,-1)\n",
    "V.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "       [1.66918947e-095],\n",
       "       [1.15081886e-119],\n",
       "       [1.06718962e-123],\n",
       "       [1.13524468e-075],\n",
       "       [2.46776149e-059]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(V*Leval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "CE-based IS stage: \n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'Wt_fun' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-9-40e3730fdb85>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     87\u001b[0m \u001b[1;31m#     beta_new = sp.optimize.fmaxbound(fmax,beta_t[t],1)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     88\u001b[0m     \u001b[1;31m# Update W_t\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 89\u001b[1;33m     \u001b[0mW_t\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mWt_fun\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbeta_new\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     90\u001b[0m     \u001b[1;31m# Parameter update: closed form\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     91\u001b[0m     \u001b[0mmu_U\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mW_t\u001b[0m\u001b[1;33m@\u001b[0m\u001b[0mU\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mW_t\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'Wt_fun' is not defined"
     ]
    }
   ],
   "source": [
    "## Self version\n",
    "# Parameter definition\n",
    "# Target distribution\n",
    "#  Parameter definition\n",
    "# This is an example where prior p(mu) ~ N(0,1),\n",
    "mu_theta_prior, sigma_theta_prior = -10, 1\n",
    "prior = lambda theta: sp.stats.norm.pdf(theta,loc = mu_theta_prior, scale = sigma_theta_prior)\n",
    "log_prior = lambda theta: sp.stats.norm.logpdf(theta,loc=mu_theta_prior,scale = sigma_theta_prior)\n",
    "theta_prior = ERADist(\"Normal\",\"MOM\",[mu_theta_prior, sigma_theta_prior])\n",
    "# Likelihood functions p(D|mu) ~ normal\n",
    "data = np.random.randn(10)\n",
    "# Likelihood function\n",
    "def Likelihood(theta):\n",
    "    total_likelihood = 1\n",
    "    sigma_X  = 1\n",
    "    for i in range(data.size):\n",
    "        total_likelihood = total_likelihood*sp.stats.norm.pdf(data[i],loc = theta, scale = sigma_X)\n",
    "    return total_likelihood\n",
    "def log_Likelihood(theta):\n",
    "    total_likelihood = 0\n",
    "    sigma_X  = 1\n",
    "    for i in range(data.size):\n",
    "        total_likelihood = total_likelihood+sp.stats.norm.logpdf(data[i],loc = theta, scale = sigma_X)\n",
    "    return total_likelihood\n",
    "def target_dist_t(theta,beta_t):\n",
    "    return prior(theta)*(Likelihood(theta))**beta_t\n",
    "def log_target_dist_t(theta,beta_t):\n",
    "    return log_prior(theta)+beta_t*log_Likelihood(theta)\n",
    "\n",
    "# # Posterior distribution\n",
    "# def target_dist(theta):\n",
    "#     return prior(theta)*Likelihood(theta)\n",
    "\n",
    "# def log_target_dist(theta):\n",
    "#     return log_prior(theta)+log_Likelihood(theta)\n",
    "N = 1000\n",
    "dim = 1\n",
    "max_it = 50\n",
    "CV_target = 1.5\n",
    "print('\\nCE-based IS stage: ')\n",
    "# transform the prior,likelihood and posterior distribution to the normal space\n",
    "# Prior transformation\n",
    "# Here X~ N(mu_X,sigma_X)\n",
    "# U = (X-mu_X)/sigma_X; X = mu_X + sigma_X*U\n",
    "x2u_prior = lambda x: (x-mu_theta_prior)/sigma_theta_prior\n",
    "u2x_prior = lambda u: mu_theta_prior+sigma_theta_prior*u\n",
    "# Likelihood in transformed space\n",
    "L_transformed = lambda u: Likelihood(u2x_prior(u))\n",
    "N_tot = 0 # Total number of samples\n",
    "# Definition of parameters of random variables\n",
    "mu_init = np.zeros(dim)\n",
    "si_init = np.identity(dim)\n",
    "beta_t = np.zeros(max_it)\n",
    "samplesU = list()\n",
    "# CE procedure (multinormal parametric family)\n",
    "mu_U = mu_init\n",
    "si_U = si_init\n",
    "# Iteration\n",
    "for t in range(max_it):\n",
    "    # Generate samples and save them\n",
    "    U = sp.stats.multivariate_normal.rvs(mean= mu_U,cov=si_U, size =N).reshape(-1,dim)\n",
    "    samplesU.append(U.T)\n",
    "    # Count generated samples\n",
    "    N_tot += N\n",
    "    # Evaluate the likelihood function\n",
    "    Leval = Likelihood(u2x_prior(U)) \n",
    "    # Initalize beta, beta increases from 0 to 1\n",
    "    if t == 0:\n",
    "        beta_t[t] = 0\n",
    "    else:\n",
    "        beta_t[t] = beta_new\n",
    "    # calculating h for the likelihood ratio\n",
    "    h = sp.stats.multivariate_normal.pdf(U,mu_U,si_U)\n",
    "    phi = sp.stats.multivariate_normal.pdf(U,mean=np.zeros(dim),cov=np.identity(dim))\n",
    "    # Likelihood ratio for the original CE weight\n",
    "    W = phi/h\n",
    "    # improved CE Likelihood weight W_t = W*l**Beta_t\n",
    "    W_t = W.reshape(N,-1)*Leval**beta_t[t]\n",
    "#     # CV of W_t\n",
    "#     delta_Wt = np.std(W_t)/np.mean(W_t)\n",
    "#     if delta_Wt <= CV_target:\n",
    "#         break\n",
    "#     # Solve the optimisation problem\n",
    "#     Wt_fun = lambda beta: W*Leval**beta\n",
    "#     CV_Wt_fun = lambda beta:np.std(Wt_fun(beta))/np.mean(Wt_fun(beta))\n",
    "#     fmax = lambda beta: abs(CV_Wt_fun(beta)-CV_target)\n",
    "#     beta_new = sp.optimize.fmaxbound(fmax,beta_t[t],1)\n",
    "    # Update W_t\n",
    "    W_t = Wt_fun(beta_new)\n",
    "    # Parameter update: closed form\n",
    "    mu_U = W_t@U/sum(W_t)\n",
    "    Xtmp = U-mu_U\n",
    "    Xo = Xtmp *np.tile(np.sqrt(W_t),(dim,1)).T\n",
    "    Si_U = np.matmul(Xo.T,Xo)/np.sum(W_t)+1e-6*np.identity(dim)\n",
    "#total levels\n",
    "lv = t\n",
    "# Calculation of the integral of the posterior = 1\n",
    "Integral = sum(W_t)/N\n",
    "# Calculation of the integral of the target_dist\n",
    "#Integral_target = \n",
    "# Transform the samples to the physical/ original space\n",
    "samplesX = list()\n",
    "for i in range(lv):\n",
    "    samplesX.append(u2x_prior(samplesU[i]))\n",
    "# Plot samples \n",
    "if dim == 1:\n",
    "    nnp = 200\n",
    "    xx = np.linspace(-6,6,nnp)\n",
    "    for sample in samplesU:\n",
    "        plt.plot(*sample,\".\",markersize=2)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# MCMC based method\n",
    "N_MCMC = 1000\n",
    "# Sample generation\n",
    "theta_current = mu_theta_prior\n",
    "sp = mu_theta_prior\n",
    "sigma = 2.4\n",
    "x = np.zeros((N_MCMC,1))\n",
    "x[0] = sp\n",
    "# generate z ~ N(0,sigma) proposal density\n",
    "z = np.random.uniform(0,1,N_MCMC)\n",
    "for i in range(N_MCMC-1):\n",
    "    # Generate Candidate sample\n",
    "    y = x[i]+z[i]\n",
    "    # evaluate the acceptance probability\n",
    "    f_y = target_dist(y[i])\n",
    "    f_x = target_dist(x[i])\n",
    "    alpha = min(1,f_y/f_x)\n",
    "    # check if sample should be accepted\n",
    "    if u[i] <= alpha:\n",
    "        x[i+1] = y\n",
    "    else:\n",
    "        x[i+1] = x[i]\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import scipy.stats as sps\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns \n",
    "from scipy.stats import norm\n",
    "sns.set_style('white')\n",
    "sns.set_context('talk')\n",
    "np.random.seed(123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.0856306 ,  0.99734545,  0.2829785 , -1.50629471, -0.57860025,\n",
       "        1.65143654, -2.42667924, -0.42891263,  1.26593626, -0.8667404 ,\n",
       "       -0.67888615, -0.09470897,  1.49138963, -0.638902  , -0.44398196,\n",
       "       -0.43435128,  2.20593008,  2.18678609,  1.0040539 ,  0.3861864 ])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This is an example where prior p(mu) ~ N(0,1),\n",
    "mu_mu = 0\n",
    "sigma_mu = 1\n",
    "prior = lambda mu: sps.norm.pdf(mu,loc = mu_mu, scale = sigma_mu)\n",
    "log_prior = lambda mu: sps.norm.logpdf(mu,loc=mu_mu,scale=sigma_mu)\n",
    "# Likelihood functions p(D|mu) ~ normal\n",
    "data = np.random.randn(20)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x19fc8409508>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu_sample = np.arange(-1,1,0.0005)\n",
    "plt.plot(mu_sample,prior(mu_sample))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x19fc8762cc8>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu_sample = np.arange(-1,1,0.01)\n",
    "plt.plot(mu_sample,log_prior(mu_sample))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11441773195529023"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5021278845126171"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.var(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.subplot()\n",
    "sns.distplot(data,kde=False,ax=ax)\n",
    "_ = ax.set(title='Histogram of observed data',xlabel='x',ylabel='# oberservations')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def likelihood(mu):\n",
    "    total_likelihood = 1\n",
    "    for i in range(data.size):\n",
    "        total_likelihood = total_likelihood*sps.norm.pdf(data[i],loc=mu,scale=1)\n",
    "    return total_likelihood\n",
    "def log_likelihood(mu):\n",
    "    total_log_likelihood = 0\n",
    "    for i in range(data.size):\n",
    "        total_log_likelihood = total_log_likelihood+sps.norm.logpdf(data[i],loc=mu,scale=1)\n",
    "    return total_log_likelihood\n",
    "def target_dist(mu):\n",
    "    return likelihood(mu)*prior(mu)\n",
    "def log_target_dist(mu):\n",
    "    return log_likelihood(mu)+log_prior(mu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Prior\n",
    "sns.distplot(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x19fc880ab48>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu_sample = np.arange(-1,1,0.01)\n",
    "plt.plot(mu_sample,prior(mu_sample),label='prior_dist')\n",
    "plt.plot(mu_sample,likelihood(mu_sample),label='likelihood')\n",
    "plt.plot(mu_sample,target_dist(mu_sample),label='target_dist')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1deb2bf5b88>"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu_sample = np.arange(-1,1,0.01)\n",
    "plt.plot(mu_sample,log_prior(mu_sample),label='prior_dist')\n",
    "plt.plot(mu_sample,log_likelihood(mu_sample),label='likelihood')\n",
    "plt.plot(mu_sample,log_target_dist(mu_sample),label='target_dist')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1deb1a26248>]"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Likelihood\n",
    "mu_sample = np.arange(-1,1,0.01)\n",
    "plt.plot(mu_sample,log_likelihood(mu_sample))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (20,) (200,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-39-719135759d3e>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[1;31m# x = np.linspace(-1,1,500)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0.01\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 5\u001b[1;33m \u001b[0mlikelihood\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m<ipython-input-39-719135759d3e>\u001b[0m in \u001b[0;36m<lambda>\u001b[1;34m(mu)\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m#ax = plt.subplot()\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mlikelihood\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0mmu\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0msp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstats\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnorm\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmu\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpdf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mprod\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[1;31m# x = np.linspace(-1,1,500)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0.01\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mlikelihood\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\scipy\\stats\\_distn_infrastructure.py\u001b[0m in \u001b[0;36mpdf\u001b[1;34m(self, x)\u001b[0m\n\u001b[0;32m    434\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    435\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mpdf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m   \u001b[1;31m# raises AttributeError in frozen discrete distribution\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 436\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdist\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpdf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mkwds\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    437\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    438\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mlogpdf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\scipy\\stats\\_distn_infrastructure.py\u001b[0m in \u001b[0;36mpdf\u001b[1;34m(self, x, *args, **kwds)\u001b[0m\n\u001b[0;32m   1758\u001b[0m         \u001b[0margs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtuple\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmap\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0masarray\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1759\u001b[0m         \u001b[0mdtyp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfind_common_type\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfloat64\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1760\u001b[1;33m         \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mloc\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mscale\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdtyp\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1761\u001b[0m         \u001b[0mcond0\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_argcheck\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m&\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mscale\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1762\u001b[0m         \u001b[0mcond1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_support_mask\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m&\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mscale\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: operands could not be broadcast together with shapes (20,) (200,) "
     ]
    }
   ],
   "source": [
    "#ax = plt.subplot()\n",
    "likelihood = lambda mu: sp.stats.norm(mu,1).pdf(data).prod()\n",
    "# x = np.linspace(-1,1,500)\n",
    "x = np.arange(-1,1,0.01)\n",
    "likelihood(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def calc_posterior_analytical(data,x,mu_0,sigma_0):# (sampled data,prior parameter)\n",
    "    sigma = 1.# Assume we only have one parameter here mu\n",
    "    # here sigma, mu are two parameters\n",
    "    # mu_0  is mu_prior_mu\n",
    "    # sigma_0 is the standard deviation of mu_prior_std\n",
    "    n = len(data)\n",
    "    mu_post = mu_0*(1/sigma_0**2/(1/sigma_0**2+n/sigma**2))+data.sum()*(1/sigma**2/(1/sigma_0**2+n/sigma**2))\n",
    "    sigma_post = 1/(1/sigma_0**2+n/sigma**2)\n",
    "    return norm(mu_post,np.sqrt(sigma_post)).pdf(x)\n",
    "likelihood = lambda mu: sp.stats.norm(mu,1).pdf(data).prod()\n",
    "ax = plt.subplot()\n",
    "x = np.linspace(-1,1,500)\n",
    "#L = likelihood(x)\n",
    "posterior_analytical = calc_posterior_analytical(data,x,0.,1.)\n",
    "ax.plot(x,posterior_analytical)  \n",
    "ax.set(xlabel='mu',ylabel='belief',title='Analytical posterior')\n",
    "sns.despine()                                                                    \n",
    "                                                        \n",
    "                                                                        \n",
    "                                                                    \n",
    "                                                                        \n",
    "                                                                        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00024215446746848768"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## MCMC sampling\n",
    "mu_current = 1\n",
    "proposal_width = 0.5\n",
    "mu_proposal = sp.stats.norm(mu_current, proposal_width).rvs()\n",
    "mu_proposal\n",
    "#proposal =sp.stats.norm(mu_current,proposal_width).rvs()\n",
    "likelihood_current = norm(mu_current,1).pdf(data).prod()\n",
    "likelihood_proposal = norm(mu_proposal,1).pdf(data).prod()\n",
    "# prior probability of the current and proposed mu\n",
    "mu_prior_mu=0\n",
    "mu_prior_sd = 1.\n",
    "prior_current = norm(mu_prior_mu,mu_prior_sd).pdf(mu_current)\n",
    "prior_proposal = norm(mu_prior_mu,mu_prior_sd).pdf(mu_proposal)\n",
    "p_current = likelihood_current * prior_current \n",
    "p_proposal = likelihood_proposal * prior_proposal\n",
    "# Accept proposal?\n",
    "p_accept = p_proposal/p_current\n",
    "accept = np.random.rand()<p_accept\n",
    "p_proposal/p_current"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.04532638, 0.39894087, 0.30851079, 0.01725428, 0.11475821,\n",
       "       0.32267059, 0.00112496, 0.14372778, 0.38508177, 0.06985746,\n",
       "       0.09746442, 0.21912074, 0.35357119, 0.10414841, 0.14065004,\n",
       "       0.14261304, 0.19280572, 0.19727252, 0.398939  , 0.33044267])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likelihood_current = norm(mu_current,1).pdf(data)\n",
    "likelihood_current"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2262032783415876e-18"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likelihood_current = norm(mu_current,1).pdf(data).prod()\n",
    "likelihood_current"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 4, 6])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([2,4,6])\n",
    "a\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "48"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.prod()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sampler(data, samples=4,mu_init=5,proposal_width =0.5 ,plot=False,mu_prior_mu = 0, mu_prior_sd =1.):\n",
    "    mu_current = mu_init\n",
    "    posterior = [mu_current]\n",
    "    for i in range(samples):\n",
    "        # Suggest new position\n",
    "        mu_proposal = norm(mu_current, proposal_width).rvs()\n",
    "        # Compute likelihood by multiplying probabilities of each data point\n",
    "        likelihood_current = norm(mu_current,1).pdf(data).prod()\n",
    "        likelihood_proposal = norm(mu_proposal,1).pdf(data).prod()\n",
    "        # Compute prior probability of current and proposed mu\n",
    "        prior_current = norm(mu_prior_mu, mu_prior_sd).pdf(mu_current)\n",
    "        prior_proposal = norm(mu_prior_mu, mu_prior_sd).pdf(mu_proposal)\n",
    "        p_current = likelihood_current* prior_current\n",
    "        p_proposal = likelihood_proposal*prior_proposal\n",
    "        # Accept proposal?\n",
    "        p_accept = p_proposal/p_current\n",
    "        # Usually would include prior probability, which we neglect here for simplicity\n",
    "        accept = np.random.rand()<p_accept\n",
    "        if plot:\n",
    "            plot_proposal(mu_current,mu_proposal,mu_prior_mu,mu_prior_sd,data,accept,posterior,i)\n",
    "        if accept:\n",
    "            # Update position\n",
    "            mu_current = mu_proposal\n",
    "        posterior.append(mu_current)\n",
    "    return np.array(posterior)\n",
    "# # Function to display\n",
    "# def plot_proposal(mu_current, mu_proposal, mu_prior_mu, mu_prior_sd, data, accepted, trace, i):\n",
    "#     from copy import copy\n",
    "#     trace = copy(trace)\n",
    "#     fig,(ax1,ax2，ax3,ax4)=plt.subplot.(ncols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "posterior = sampler(data, samples=15000,mu_init=1.)\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(posterior)\n",
    "_ = ax.set(xlabel='sample',ylabel='mu')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1deb151d0c8>"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.subplot()\n",
    "sns.distplot(posterior[500:],ax=ax,label='estimated posterior')\n",
    "x = np.linspace(-0.5,0.5,500)\n",
    "post = calc_posterior_analytical(data,x,0,1)\n",
    "ax.plot(x,post,'g',label='analytic posterior')\n",
    "_=ax.set(xlabel='mu',ylabel='belief')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# above the proposal width is set to be 0.5. That turned out to be a good value.\n",
    "# In general you don not want the width to be too narrow because your sampling will be inefficient as it takes a long time to explore the whole parameter space and shows the typical random walk behavior\n",
    "posterior_small = sampler(data, samples=15000,mu_init=1.0,proposal_width=0.01)\n",
    "fig,ax = plt.subplots()\n",
    "ax.plot(posterior_small)\n",
    "_ = ax.set(xlabel='sample',ylabel='mu')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# But you also do not want a large width which will never accept a jump\n",
    "posterior_large = sampler(data,samples=15000,mu_init=1.,proposal_width = 3.)\n",
    "fig,ax = plt.subplots()\n",
    "ax.plot(posterior_large)\n",
    "_ = ax.set(xlabel='sample',ylabel='mu')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Note that we are still sampling from our target posterior distribution as guaranteed by the mathematical proof, just less efficient\n",
    "sns.distplot(posterior_small[1000:],label='small step size')\n",
    "sns.distplot(posterior_large[1000:],label='large step size')\n",
    "_ = plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "__init__() got an unexpected keyword argument 'obeservation'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-20-a73d94fc22d1>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      3\u001b[0m     \u001b[0mmu\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mNormal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'mu'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m     \u001b[0msigma\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m1.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 5\u001b[1;33m     \u001b[0mreturns\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mNormal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'returns'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mmu\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmu\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0msd\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msigma\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mobeservation\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      6\u001b[0m     \u001b[0mstep\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mMetropolis\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      7\u001b[0m     \u001b[0mtrace\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msample\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m15000\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mstep\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pymc3\\distributions\\distribution.py\u001b[0m in \u001b[0;36m__new__\u001b[1;34m(cls, name, *args, **kwargs)\u001b[0m\n\u001b[0;32m     44\u001b[0m                 \u001b[1;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"observed needs to be data but got: {}\"\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     45\u001b[0m             \u001b[0mtotal_size\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'total_size'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 46\u001b[1;33m             \u001b[0mdist\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcls\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdist\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     47\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mmodel\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mVar\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mname\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdist\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtotal_size\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     48\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pymc3\\distributions\\distribution.py\u001b[0m in \u001b[0;36mdist\u001b[1;34m(cls, *args, **kwargs)\u001b[0m\n\u001b[0;32m     55\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mdist\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     56\u001b[0m         \u001b[0mdist\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mobject\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__new__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 57\u001b[1;33m         \u001b[0mdist\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     58\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mdist\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     59\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pymc3\\distributions\\continuous.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, mu, sigma, tau, sd, **kwargs)\u001b[0m\n\u001b[0;32m    473\u001b[0m         \u001b[0massert_negative_support\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtau\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'tau'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'Normal'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    474\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 475\u001b[1;33m         \u001b[0msuper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    476\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    477\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mrandom\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpoint\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msize\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pymc3\\distributions\\distribution.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, shape, dtype, defaults, *args, **kwargs)\u001b[0m\n\u001b[0;32m    191\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mdtype\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    192\u001b[0m             \u001b[0mdtype\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtheano\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mconfig\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfloatX\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 193\u001b[1;33m         \u001b[0msuper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdefaults\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdefaults\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    194\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    195\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: __init__() got an unexpected keyword argument 'obeservation'"
     ]
    }
   ],
   "source": [
    "import pymc3 as pm\n",
    "with pm.Model():\n",
    "    mu = pm.Normal('mu',0,1)\n",
    "    sigma = 1.\n",
    "    returns = pm.Normal('returns',mu=mu,sd = sigma,obeservation=data)\n",
    "    step = pm.Metropolis()\n",
    "    trace = pm.sample(15000,step)\n",
    "sns.distplot(trace[2000:]['mu'],label='PyMC3 sampler')\n",
    "sns.distplot(posterior[500:],label='Hand-written sampler')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "module 'statsmodels' has no attribute 'tsa'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-1-2985cc853c99>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mstatsmodels\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mstatsmodels\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtsa\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapi\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstattools\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0macf\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m: module 'statsmodels' has no attribute 'tsa'"
     ]
    }
   ],
   "source": [
    "import statsmodels\n",
    "statsmodels.tsa.api.stattools.acf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'numpy.ndarray' object has no attribute 'corr'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-26-84ea82807d7e>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      7\u001b[0m \u001b[0mlags\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m100\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m \u001b[0mfig\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0max\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubplots\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 9\u001b[1;33m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlags\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mpd\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mSeries\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mautocorr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mposterior_large\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mlags\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlabel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'large step size'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     10\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlags\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mpd\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mSeries\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mautocorr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mposterior_small\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mlags\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlabel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'small step size'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     11\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-26-84ea82807d7e>\u001b[0m in \u001b[0;36m<listcomp>\u001b[1;34m(.0)\u001b[0m\n\u001b[0;32m      7\u001b[0m \u001b[0mlags\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m100\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m \u001b[0mfig\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0max\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubplots\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 9\u001b[1;33m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlags\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mpd\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mSeries\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mautocorr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mposterior_large\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mlags\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlabel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'large step size'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     10\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlags\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mpd\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mSeries\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mautocorr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mposterior_small\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mlags\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlabel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'small step size'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     11\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pandas\\core\\series.py\u001b[0m in \u001b[0;36mautocorr\u001b[1;34m(self, lag)\u001b[0m\n\u001b[0;32m   2507\u001b[0m         \u001b[0mnan\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2508\u001b[0m         \"\"\"\n\u001b[1;32m-> 2509\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcorr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshift\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlag\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2510\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2511\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mother\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'numpy.ndarray' object has no attribute 'corr'"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# with more samples this will eventually look like the true posteriro. The key is that we want our samples to be independent of each other\n",
    "# One commen metric to evaluate the efficiency of our sampler is the autocorrelation\n",
    "# how correlated a sample i is to sample i-1, i-1 etc\n",
    "#from pymc3.stats import autocorr ? How to plot the autocorrelation\n",
    "#statsmodels.tsa.api.stattools.acf\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "lags = np.arange(1,100)\n",
    "fig,ax = plt.subplots()\n",
    "ax.plot(lags,[pd.Series.autocorr(posterior_large,i) for i in lags],label='large step size')\n",
    "ax.plot(lags,[pd.Series.autocorr(posterior_small,i) for i in lags],label='small step size')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10355263309024071"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series([0.25,0.5,0.2,-0.05])\n",
    "s.autocorr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named '__main__.model'; '__main__' is not a package",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-4-29592e22b343>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      7\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mwarnings\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mcollections\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mnamedtuple\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 9\u001b[1;33m \u001b[1;32mfrom\u001b[0m \u001b[1;33m.\u001b[0m\u001b[0mmodel\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mmodelcontext\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     10\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[1;33m.\u001b[0m\u001b[0mutil\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mget_default_varnames\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     11\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mpymc3\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mpm\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m: No module named '__main__.model'; '__main__' is not a package"
     ]
    }
   ],
   "source": [
    "\"\"\"Statistical utility functions for PyMC\"\"\"\n",
    " \n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import itertools\n",
    "from tqdm import tqdm\n",
    "import warnings\n",
    "from collections import namedtuple\n",
    "from .model import modelcontext\n",
    "from .util import get_default_varnames\n",
    "import pymc3 as pm\n",
    "from pymc3.theanof import floatX\n",
    " \n",
    "from scipy.misc import logsumexp\n",
    "from scipy.stats import dirichlet\n",
    "from scipy.optimize import minimize\n",
    " \n",
    " \n",
    "__all__ = ['autocorr', 'autocov', 'dic', 'bpic', 'waic', 'loo', 'hpd', 'quantiles',\n",
    "           'mc_error', 'summary', 'df_summary', 'compare', 'bfmi', 'r2_score']\n",
    " \n",
    "def statfunc(f):\n",
    "    \"\"\"\n",
    "    Decorator for statistical utility function to automatically\n",
    "    extract the trace array from whatever object is passed.\n",
    "    \"\"\"\n",
    " \n",
    "    def wrapped_f(pymc3_obj, *args, **kwargs):\n",
    "        try:\n",
    "            vars = kwargs.pop('vars',  pymc3_obj.varnames)\n",
    "            chains = kwargs.pop('chains', pymc3_obj.chains)\n",
    "        except AttributeError:\n",
    "            # If fails, assume that raw data was passed.\n",
    "            return f(pymc3_obj, *args, **kwargs)\n",
    " \n",
    "        burn = kwargs.pop('burn', 0)\n",
    "        thin = kwargs.pop('thin', 1)\n",
    "        combine = kwargs.pop('combine', False)\n",
    "        # Remove outer level chain keys if only one chain)\n",
    "        squeeze = kwargs.pop('squeeze', True)\n",
    " \n",
    "        results = {chain: {} for chain in chains}\n",
    "        for var in vars:\n",
    "            samples = pymc3_obj.get_values(var, chains=chains, burn=burn,\n",
    "                                           thin=thin, combine=combine,\n",
    "                                           squeeze=False)\n",
    "            for chain, data in zip(chains, samples):\n",
    "                results[chain][var] = f(np.squeeze(data), *args, **kwargs)\n",
    " \n",
    "        if squeeze and (len(chains) == 1 or combine):\n",
    "            results = results[chains[0]]\n",
    "        return results\n",
    " \n",
    "    wrapped_f.__doc__ = f.__doc__\n",
    "    wrapped_f.__name__ = f.__name__\n",
    " \n",
    "    return wrapped_f\n",
    " \n",
    " \n",
    "@statfunc\n",
    "def autocorr(x, lag=1):\n",
    "    \"\"\"Sample autocorrelation at specified lag.\n",
    " \n",
    "    Parameters\n",
    "    ----------\n",
    "    x : Numpy array\n",
    "        An array containing MCMC samples\n",
    "    lag : int\n",
    "        The desidered lag to take in consideration\n",
    "    \"\"\"\n",
    "    S = autocov(x, lag)\n",
    "    return S[0, 1] / np.sqrt(np.prod(np.diag(S)))\n",
    " \n",
    " \n",
    "@statfunc\n",
    "def autocov(x, lag=1):\n",
    "    \"\"\"Sample autocovariance at specified lag.\n",
    " \n",
    "    Parameters\n",
    "    ----------\n",
    "    x : Numpy array\n",
    "        An array containing MCMC samples\n",
    "    lag : int\n",
    "        The desidered lag to take in consideration\n",
    " \n",
    "    Returns\n",
    "    -------\n",
    "    2x2 matrix with the variances of\n",
    "    x[:-lag] and x[lag:] in the diagonal and the autocovariance\n",
    "    on the off-diagonal.\n",
    "    \"\"\"\n",
    "    x = np.asarray(x)\n",
    " \n",
    "    if not lag:\n",
    "        return 1\n",
    "    if lag < 0:\n",
    "        raise ValueError(\"Autocovariance lag must be a positive integer\")\n",
    "    return np.cov(x[:-lag], x[lag:], bias=1)\n",
    " \n",
    "def dic(trace, model=None):\n",
    "    \"\"\"Calculate the deviance information criterion of the samples in trace from model\n",
    "    Read more theory here - in a paper by some of the leading authorities on model selection -\n",
    "    dx.doi.org/10.1111/1467-9868.00353\n",
    " \n",
    "    Parameters\n",
    "    ----------\n",
    "    trace : result of MCMC run\n",
    "    model : PyMC Model\n",
    "        Optional model. Default None, taken from context.\n",
    " \n",
    "    Returns\n",
    "    -------\n",
    "    z : float\n",
    "        The deviance information criterion of the model and trace\n",
    "    \"\"\"\n",
    "    warnings.warn(\"dic has been deprecated. Use `waic` or `loo` instead.\", DeprecationWarning,\n",
    "                  stacklevel=2)\n",
    " \n",
    "    model = modelcontext(model)\n",
    "    logp = model.logp\n",
    " \n",
    "    mean_deviance = -2 * np.mean([logp(pt) for pt in trace])\n",
    " \n",
    "    free_rv_means = {rv.name: trace[rv.name].mean(\n",
    "        axis=0) for rv in model.free_RVs}\n",
    "    deviance_at_mean = -2 * logp(free_rv_means)\n",
    " \n",
    "    return 2 * mean_deviance - deviance_at_mean\n",
    " \n",
    "def _log_post_trace(trace, model=None, progressbar=False):\n",
    "    \"\"\"Calculate the elementwise log-posterior for the sampled trace.\n",
    " \n",
    "    Parameters\n",
    "    ----------\n",
    "    trace : result of MCMC run\n",
    "    model : PyMC Model\n",
    "        Optional model. Default None, taken from context.\n",
    "    progressbar: bool\n",
    "        Whether or not to display a progress bar in the command line. The\n",
    "        bar shows the percentage of completion, the evaluation speed, and\n",
    "        the estimated time to completion\n",
    " \n",
    "    Returns\n",
    "    -------\n",
    "    logp : array of shape (n_samples, n_observations)\n",
    "        The contribution of the observations to the logp of the whole model.\n",
    "    \"\"\"\n",
    "    model = modelcontext(model)\n",
    "    cached = [(var, var.logp_elemwise) for var in model.observed_RVs]\n",
    " \n",
    "    def logp_vals_point(pt):\n",
    "        if len(model.observed_RVs) == 0:\n",
    "            return floatX(np.array([], dtype='d'))\n",
    " \n",
    "        logp_vals = []\n",
    "        for var, logp in cached:\n",
    "            logp = logp(pt)\n",
    "            if var.missing_values:\n",
    "                logp = logp[~var.observations.mask]\n",
    "            logp_vals.append(logp.ravel())\n",
    " \n",
    "        return np.concatenate(logp_vals)\n",
    " \n",
    "    try:\n",
    "        points = trace.points()\n",
    "    except AttributeError:\n",
    "        points = trace\n",
    " \n",
    "    points = tqdm(points) if progressbar else points\n",
    " \n",
    "    try:\n",
    "        logp = (logp_vals_point(pt) for pt in points)\n",
    "        return np.stack(logp)\n",
    "    finally:\n",
    "        if progressbar:\n",
    "            points.close()\n",
    " \n",
    " \n",
    "def waic(trace, model=None, pointwise=False, progressbar=False):\n",
    "    \"\"\"Calculate the widely available information criterion, its standard error\n",
    "    and the effective number of parameters of the samples in trace from model.\n",
    "    Read more theory here - in a paper by some of the leading authorities on\n",
    "    model selection - dx.doi.org/10.1111/1467-9868.00353\n",
    " \n",
    "    Parameters\n",
    "    ----------\n",
    "    trace : result of MCMC run\n",
    "    model : PyMC Model\n",
    "        Optional model. Default None, taken from context.\n",
    "    pointwise: bool\n",
    "        if True the pointwise predictive accuracy will be returned.\n",
    "        Default False\n",
    "    progressbar: bool\n",
    "        Whether or not to display a progress bar in the command line. The\n",
    "        bar shows the percentage of completion, the evaluation speed, and\n",
    "        the estimated time to completion\n",
    " \n",
    "    Returns\n",
    "    -------\n",
    "    namedtuple with the following elements:\n",
    "    waic: widely available information criterion\n",
    "    waic_se: standard error of waic\n",
    "    p_waic: effective number parameters\n",
    "    waic_i: and array of the pointwise predictive accuracy, only if pointwise True\n",
    "    \"\"\"\n",
    "    model = modelcontext(model)\n",
    " \n",
    "    log_py = _log_post_trace(trace, model, progressbar=progressbar)\n",
    "    if log_py.size == 0:\n",
    "        raise ValueError('The model does not contain observed values.')\n",
    " \n",
    "    lppd_i = logsumexp(log_py, axis=0, b=1.0 / log_py.shape[0])\n",
    " \n",
    "    vars_lpd = np.var(log_py, axis=0)\n",
    "    if np.any(vars_lpd > 0.4):\n",
    "        warnings.warn(\"\"\"For one or more samples the posterior variance of the\n",
    "        log predictive densities exceeds 0.4. This could be indication of\n",
    "        WAIC starting to fail see http://arxiv.org/abs/1507.04544 for details\n",
    "        \"\"\")\n",
    "    waic_i = - 2 * (lppd_i - vars_lpd)\n",
    " \n",
    "    waic_se = np.sqrt(len(waic_i) * np.var(waic_i))\n",
    " \n",
    "    waic = np.sum(waic_i)\n",
    " \n",
    "    p_waic = np.sum(vars_lpd)\n",
    " \n",
    "    if pointwise:\n",
    "        WAIC_r = namedtuple('WAIC_r', 'WAIC, WAIC_se, p_WAIC, WAIC_i')\n",
    "        return WAIC_r(waic, waic_se, p_waic, waic_i)\n",
    "    else:\n",
    "        WAIC_r = namedtuple('WAIC_r', 'WAIC, WAIC_se, p_WAIC')\n",
    "        return WAIC_r(waic, waic_se, p_waic)\n",
    " \n",
    " \n",
    "def loo(trace, model=None, pointwise=False, reff=None, progressbar=False):\n",
    "    \"\"\"Calculates leave-one-out (LOO) cross-validation for out of sample\n",
    "    predictive model fit, following Vehtari et al. (2015). Cross-validation is\n",
    "    computed using Pareto-smoothed importance sampling (PSIS).\n",
    " \n",
    "    Parameters\n",
    "    ----------\n",
    "    trace : result of MCMC run\n",
    "    model : PyMC Model\n",
    "        Optional model. Default None, taken from context.\n",
    "    pointwise: bool\n",
    "        if True the pointwise predictive accuracy will be returned.\n",
    "        Default False\n",
    "    reff : float\n",
    "        relative MCMC efficiency, `effective_n / n` i.e. number of effective\n",
    "        samples divided by the number of actual samples. Computed from trace by\n",
    "        default.\n",
    "    progressbar: bool\n",
    "        Whether or not to display a progress bar in the command line. The\n",
    "        bar shows the percentage of completion, the evaluation speed, and\n",
    "        the estimated time to completion\n",
    " \n",
    "    Returns\n",
    "    -------\n",
    "    namedtuple with the following elements:\n",
    "    loo: approximated Leave-one-out cross-validation\n",
    "    loo_se: standard error of loo\n",
    "    p_loo: effective number of parameters\n",
    "    loo_i: array of pointwise predictive accuracy, only if pointwise True\n",
    "    \"\"\"\n",
    "    model = modelcontext(model)\n",
    " \n",
    "    if reff is None:\n",
    "        if trace.nchains == 1:\n",
    "            reff = 1.\n",
    "        else:\n",
    "            eff = pm.effective_n(trace)\n",
    "            eff_ave = pm.stats.dict2pd(eff, 'eff').mean()\n",
    "            samples = len(trace) * trace.nchains\n",
    "            reff = eff_ave / samples\n",
    " \n",
    "    log_py = _log_post_trace(trace, model, progressbar=progressbar)\n",
    "    if log_py.size == 0:\n",
    "        raise ValueError('The model does not contain observed values.')\n",
    " \n",
    "    lw, ks = _psislw(-log_py, reff)\n",
    "    lw += log_py\n",
    "    if np.any(ks > 0.7):\n",
    "        warnings.warn(\"\"\"Estimated shape parameter of Pareto distribution is\n",
    "        greater than 0.7 for one or more samples.\n",
    "        You should consider using a more robust model, this is because\n",
    "        importance sampling is less likely to work well if the marginal\n",
    "        posterior and LOO posterior are very different. This is more likely to\n",
    "        happen with a non-robust model and highly influential observations.\"\"\")\n",
    " \n",
    "    loo_lppd_i = - 2 * logsumexp(lw, axis=0)\n",
    "    loo_lppd = loo_lppd_i.sum()\n",
    "    loo_lppd_se = (len(loo_lppd_i) * np.var(loo_lppd_i)) ** 0.5\n",
    "    lppd = np.sum(logsumexp(log_py, axis=0, b=1. / log_py.shape[0]))\n",
    "    p_loo = lppd + (0.5 * loo_lppd)\n",
    " \n",
    "    if pointwise:\n",
    "        LOO_r = namedtuple('LOO_r', 'LOO, LOO_se, p_LOO, LOO_i')\n",
    "        return LOO_r(loo_lppd, loo_lppd_se, p_loo, loo_lppd_i)\n",
    "    else:\n",
    "        LOO_r = namedtuple('LOO_r', 'LOO, LOO_se, p_LOO')\n",
    "        return LOO_r(loo_lppd, loo_lppd_se, p_loo)\n",
    " \n",
    " \n",
    "def _psislw(lw, reff):\n",
    "    \"\"\"Pareto smoothed importance sampling (PSIS).\n",
    " \n",
    "    Parameters\n",
    "    ----------\n",
    "    lw : array\n",
    "        Array of size (n_samples, n_observations)\n",
    "    reff : float\n",
    "        relative MCMC efficiency, `effective_n / n`\n",
    " \n",
    "    Returns\n",
    "    -------\n",
    "    lw_out : array\n",
    "        Smoothed log weights\n",
    "    kss : array\n",
    "        Pareto tail indices\n",
    "    \"\"\"\n",
    "    n, m = lw.shape\n",
    " \n",
    "    lw_out = np.copy(lw, order='F')\n",
    "    kss = np.empty(m)\n",
    " \n",
    "    # precalculate constants\n",
    "    cutoff_ind = - int(np.ceil(min(n / 0.5, 3 * (n / reff) ** 0.5))) - 1\n",
    "    cutoffmin = np.log(np.finfo(float).tiny)\n",
    "    k_min = 1. / 3\n",
    " \n",
    "    # loop over sets of log weights\n",
    "    for i, x in enumerate(lw_out.T):\n",
    "        # improve numerical accuracy\n",
    "        x -= np.max(x)\n",
    "        # sort the array\n",
    "        x_sort_ind = np.argsort(x)\n",
    "        # divide log weights into body and right tail\n",
    "        xcutoff = max(x[x_sort_ind[cutoff_ind]], cutoffmin)\n",
    " \n",
    "        expxcutoff = np.exp(xcutoff)\n",
    "        tailinds, = np.where(x > xcutoff)\n",
    "        x2 = x[tailinds]\n",
    "        n2 = len(x2)\n",
    "        if n2 <= 4:\n",
    "            # not enough tail samples for gpdfit\n",
    "            k = np.inf\n",
    "        else:\n",
    "            # order of tail samples\n",
    "            x2si = np.argsort(x2)\n",
    "            # fit generalized Pareto distribution to the right tail samples\n",
    "            x2 = np.exp(x2) - expxcutoff\n",
    "            k, sigma = _gpdfit(x2[x2si])\n",
    " \n",
    "        if k >= k_min and not np.isinf(k):\n",
    "            # no smoothing if short tail or GPD fit failed\n",
    "            # compute ordered statistic for the fit\n",
    "            sti = np.arange(0.5, n2) / n2\n",
    "            qq = _gpinv(sti, k, sigma)\n",
    "            qq = np.log(qq + expxcutoff)\n",
    "            # place the smoothed tail into the output array\n",
    "            x[tailinds[x2si]] = qq\n",
    "            # truncate smoothed values to the largest raw weight 0\n",
    "            x[x > 0] = 0\n",
    "        # renormalize weights\n",
    "        x -= logsumexp(x)\n",
    "        # store tail index k\n",
    "        kss[i] = k\n",
    " \n",
    "    return lw_out, kss\n",
    " \n",
    "def _gpdfit(x):\n",
    "    \"\"\"Estimate the parameters for the Generalized Pareto Distribution (GPD)\n",
    " \n",
    "    Empirical Bayes estimate for the parameters of the generalized Pareto\n",
    "    distribution given the data.\n",
    " \n",
    "    Parameters\n",
    "    ----------\n",
    "    x : array\n",
    "        sorted 1D data array\n",
    " \n",
    "    Returns\n",
    "    -------\n",
    "    k : float\n",
    "        estimated shape parameter\n",
    "    sigma : float\n",
    "        estimated scale parameter\n",
    "    \"\"\"\n",
    "    prior_bs = 3\n",
    "    prior_k = 10\n",
    "    n = len(x)\n",
    "    m = 30 + int(n**0.5)\n",
    " \n",
    "    bs = 1 - np.sqrt(m / (np.arange(1, m + 1, dtype=float) - 0.5))\n",
    "    bs /= prior_bs * x[int(n/4 + 0.5) - 1]\n",
    "    bs += 1 / x[-1]\n",
    " \n",
    "    ks = np.log1p(-bs[:, None] * x).mean(axis=1)\n",
    "    L = n * (np.log(-(bs / ks)) - ks - 1)\n",
    "    w = 1 / np.exp(L - L[:, None]).sum(axis=1)\n",
    " \n",
    "    # remove negligible weights\n",
    "    dii = w >= 10 * np.finfo(float).eps\n",
    "    if not np.all(dii):\n",
    "        w = w[dii]\n",
    "        bs = bs[dii]\n",
    "    # normalise w\n",
    "    w /= w.sum()\n",
    " \n",
    "    # posterior mean for b\n",
    "    b = np.sum(bs * w)\n",
    "    # estimate for k\n",
    "    k = np.log1p(- b * x).mean()\n",
    "    # add prior for k\n",
    "    k = (n * k + prior_k * 0.5) / (n + prior_k)\n",
    "    sigma = - k / b\n",
    " \n",
    "    return k, sigma\n",
    " \n",
    "def _gpinv(p, k, sigma):\n",
    "    \"\"\"Inverse Generalized Pareto distribution function\"\"\"\n",
    "    x = np.full_like(p, np.nan)\n",
    "    if sigma <= 0:\n",
    "        return x\n",
    "    ok = (p > 0) & (p < 1)\n",
    "    if np.all(ok):\n",
    "        if np.abs(k) < np.finfo(float).eps:\n",
    "            x = - np.log1p(-p)\n",
    "        else:\n",
    "            x = np.expm1(-k * np.log1p(-p)) / k\n",
    "        x *= sigma\n",
    "    else:\n",
    "        if np.abs(k) < np.finfo(float).eps:\n",
    "            x[ok] = - np.log1p(-p[ok])\n",
    "        else:\n",
    "            x[ok] = np.expm1(-k * np.log1p(-p[ok])) / k\n",
    "        x *= sigma\n",
    "        x[p == 0] = 0\n",
    "        if k >= 0:\n",
    "            x[p == 1] = np.inf\n",
    "        else:\n",
    "            x[p == 1] = - sigma / k\n",
    " \n",
    "    return x\n",
    " \n",
    "def bpic(trace, model=None):\n",
    "    R\"\"\"Calculates Bayesian predictive information criterion n of the samples in trace from model\n",
    "    Read more theory here - in a paper by some of the leading authorities on model selection -\n",
    "    dx.doi.org/10.1080/01966324.2011.10737798\n",
    " \n",
    "    Parameters\n",
    "    ----------\n",
    "    trace : result of MCMC run\n",
    "    model : PyMC Model\n",
    "        Optional model. Default None, taken from context.\n",
    " \n",
    "    Returns\n",
    "    -------\n",
    "    z : float\n",
    "        The Bayesian predictive information criterion of the model and trace\n",
    "    \"\"\"\n",
    "    warnings.warn(\"bpic has been deprecated. Use `waic` or `loo` instead.\", DeprecationWarning,\n",
    "                  stacklevel=2)\n",
    " \n",
    "    model = modelcontext(model)\n",
    "    logp = model.logp\n",
    " \n",
    "    mean_deviance = -2 * np.mean([logp(pt) for pt in trace])\n",
    " \n",
    "    free_rv_means = {rv.name: trace[rv.name].mean(\n",
    "        axis=0) for rv in model.free_RVs}\n",
    "    deviance_at_mean = -2 * logp(free_rv_means)\n",
    " \n",
    "    return 3 * mean_deviance - 2 * deviance_at_mean\n",
    " \n",
    "def compare(traces, models, ic='WAIC', method='stacking', b_samples=1000,\n",
    "            alpha=1, seed=None, round_to=2):\n",
    "    R\"\"\"Compare models based on the widely available information criterion (WAIC)\n",
    "    or leave-one-out (LOO) cross-validation.\n",
    "    Read more theory here - in a paper by some of the leading authorities on\n",
    "    model selection - dx.doi.org/10.1111/1467-9868.00353\n",
    " \n",
    "    Parameters\n",
    "    ----------\n",
    "    traces : list of PyMC3 traces\n",
    "    models : list of PyMC3 models\n",
    "        in the same order as traces.\n",
    "    ic : string\n",
    "        Information Criterion (WAIC or LOO) used to compare models.\n",
    "        Default WAIC.\n",
    "    method : str\n",
    "        Method used to estimate the weights for each model. Available options\n",
    "        are:\n",
    "            - 'stacking' : (default) stacking of predictive distributions.\n",
    "            - 'BB-pseudo-BMA' : pseudo-Bayesian Model averaging using Akaike-type\n",
    "               weighting. The weights are stabilized using the Bayesian bootstrap\n",
    "            - 'pseudo-BMA': pseudo-Bayesian Model averaging using Akaike-type\n",
    "               weighting, without Bootstrap stabilization (not recommended)\n",
    " \n",
    "        For more information read https://arxiv.org/abs/1704.02030\n",
    "    b_samples: int\n",
    "        Number of samples taken by the Bayesian bootstrap estimation. Only\n",
    "        useful when method = 'BB-pseudo-BMA'.\n",
    "    alpha : float\n",
    "        The shape parameter in the Dirichlet distribution used for the\n",
    "        Bayesian bootstrap. Only useful when method = 'BB-pseudo-BMA'. When\n",
    "        alpha=1 (default), the distribution is uniform on the simplex. A\n",
    "        smaller alpha will keeps the final weights more away from 0 and 1.\n",
    "    seed : int or np.random.RandomState instance\n",
    "           If int or RandomState, use it for seeding Bayesian bootstrap. Only\n",
    "           useful when method = 'BB-pseudo-BMA'. Default None the global\n",
    "           np.random state is used.\n",
    "    round_to : int\n",
    "        Number of decimals used to round results (default 2).\n",
    " \n",
    "    Returns\n",
    "    -------\n",
    "    A DataFrame, ordered from lowest to highest IC. The index reflects\n",
    "    the order in which the models are passed to this function. The columns are:\n",
    "    IC : Information Criteria (WAIC or LOO).\n",
    "        Smaller IC indicates higher out-of-sample predictive fit (\"better\" model).\n",
    "        Default WAIC.\n",
    "    pIC : Estimated effective number of parameters.\n",
    "    dIC : Relative difference between each IC (WAIC or LOO)\n",
    "    and the lowest IC (WAIC or LOO).\n",
    "        It's always 0 for the top-ranked model.\n",
    "    weight: Relative weight for each model.\n",
    "        This can be loosely interpreted as the probability of each model\n",
    "        (among the compared model) given the data. By default the uncertainty\n",
    "        in the weights estimation is considered using Bayesian bootstrap.\n",
    "    SE : Standard error of the IC estimate.\n",
    "        If method = BB-pseudo-BMA these values are estimated using Bayesian\n",
    "        bootstrap.\n",
    "    dSE : Standard error of the difference in IC between each model and\n",
    "    the top-ranked model.\n",
    "        It's always 0 for the top-ranked model.\n",
    "    warning : A value of 1 indicates that the computation of the IC may not be\n",
    "        reliable see http://arxiv.org/abs/1507.04544 for details.\n",
    "    \"\"\"\n",
    "    if ic == 'WAIC':\n",
    "        ic_func = waic\n",
    "        df_comp = pd.DataFrame(index=np.arange(len(models)),\n",
    "                               columns=['WAIC', 'pWAIC', 'dWAIC', 'weight',\n",
    "                                        'SE', 'dSE', 'warning'])\n",
    " \n",
    "    elif ic == 'LOO':\n",
    "        ic_func = loo\n",
    "        df_comp = pd.DataFrame(index=np.arange(len(models)),\n",
    "                               columns=['LOO', 'pLOO', 'dLOO', 'weight',\n",
    "                                        'SE', 'dSE', 'warning'])\n",
    " \n",
    "    else:\n",
    "        raise NotImplementedError(\n",
    "            'The information criterion {} is not supported.'.format(ic))\n",
    " \n",
    "    if len(set([len(m.observed_RVs) for m in models])) != 1:\n",
    "        raise ValueError(\n",
    "            'The number of observed RVs should be the same across all models')\n",
    " \n",
    "    if method not in ['stacking', 'BB-pseudo-BMA', 'pseudo-BMA']:\n",
    "        raise ValueError('The method {}, to compute weights,'\n",
    "                         'is not supported.'.format(method))\n",
    " \n",
    "    warns = np.zeros(len(models))\n",
    " \n",
    "    c = 0\n",
    "    def add_warns(*args):\n",
    "        warns[c] = 1\n",
    " \n",
    "    with warnings.catch_warnings():\n",
    "        warnings.showwarning = add_warns\n",
    "        warnings.filterwarnings('always')\n",
    " \n",
    "        ics = []\n",
    "        for c, (t, m) in enumerate(zip(traces, models)):\n",
    "            ics.append((c, ic_func(t, m, pointwise=True)))\n",
    " \n",
    "    ics.sort(key=lambda x: x[1][0])\n",
    " \n",
    "    if method == 'stacking':\n",
    "        N, K, ic_i = _ic_matrix(ics)\n",
    "        exp_ic_i = np.exp(-0.5 * ic_i)\n",
    "        Km = K - 1\n",
    " \n",
    "        def w_fuller(w):\n",
    "            return np.concatenate((w, [max(1. - np.sum(w), 0.)]))\n",
    " \n",
    "        def log_score(w):\n",
    "            w_full = w_fuller(w)\n",
    "            score = 0.\n",
    "            for i in range(N):\n",
    "                score += np.log(np.dot(exp_ic_i[i], w_full))\n",
    "            return -score\n",
    " \n",
    "        def gradient(w):\n",
    "            w_full = w_fuller(w)\n",
    "            grad = np.zeros(Km)\n",
    "            for k in range(Km):\n",
    "                for i in range(N):\n",
    "                    grad[k] += (exp_ic_i[i, k] - exp_ic_i[i, Km]) / \\\n",
    "                        np.dot(exp_ic_i[i], w_full)\n",
    "            return -grad\n",
    " \n",
    "        theta = np.full(Km, 1. / K)\n",
    "        bounds = [(0., 1.) for i in range(Km)]\n",
    "        constraints = [{'type': 'ineq', 'fun': lambda x: -np.sum(x) + 1.},\n",
    "                       {'type': 'ineq', 'fun': lambda x: np.sum(x)}]\n",
    " \n",
    "        w = minimize(fun=log_score,\n",
    "                     x0=theta,\n",
    "                     jac=gradient,\n",
    "                     bounds=bounds,\n",
    "                     constraints=constraints)\n",
    " \n",
    "        weights = w_fuller(w['x'])\n",
    "        ses = [res[1] for _, res in ics]\n",
    " \n",
    "    elif method == 'BB-pseudo-BMA':\n",
    "        N, K, ic_i = _ic_matrix(ics)\n",
    "        ic_i = ic_i * N\n",
    " \n",
    "        b_weighting = dirichlet.rvs(alpha=[alpha] * N, size=b_samples,\n",
    "                                    random_state=seed)\n",
    "        weights = np.zeros((b_samples, K))\n",
    "        z_bs = np.zeros_like(weights)\n",
    "        for i in range(b_samples):\n",
    "            z_b = np.dot(b_weighting[i], ic_i)\n",
    "            u_weights = np.exp(-0.5 * (z_b - np.min(z_b)))\n",
    "            z_bs[i] = z_b\n",
    "            weights[i] = u_weights / np.sum(u_weights)\n",
    " \n",
    "        weights = weights.mean(0)\n",
    "        ses = z_bs.std(0)\n",
    " \n",
    "    elif method == 'pseudo-BMA':\n",
    "        min_ic = ics[0][1][0]\n",
    "        Z = np.sum([np.exp(-0.5 * (x[1][0] - min_ic)) for x in ics])\n",
    "        weights = []\n",
    "        ses = []\n",
    "        for _, res in ics:\n",
    "            weights.append(np.exp(-0.5 * (res[0] - min_ic)) / Z)\n",
    "            ses.append(res[1])\n",
    " \n",
    "    if np.any(weights):\n",
    "        for i, (idx, res) in enumerate(ics):\n",
    "            diff = res[3] - ics[0][1][3]\n",
    "            d_ic = np.sum(diff)\n",
    "            d_se = np.sqrt(len(diff) * np.var(diff))\n",
    "            se = ses[i]\n",
    "            weight = weights[i]\n",
    "            df_comp.at[idx] = (round(res[0], round_to),\n",
    "                               round(res[2], round_to),\n",
    "                               round(d_ic, round_to),\n",
    "                               round(weight, round_to),\n",
    "                               round(se, round_to),\n",
    "                               round(d_se, round_to),\n",
    "                               warns[idx])\n",
    " \n",
    "        return df_comp.sort_values(by=ic)\n",
    " \n",
    "def _ic_matrix(ics):\n",
    "    \"\"\"Store the previously computed pointwise predictive accuracy values (ics)\n",
    "    in a 2D matrix array.\n",
    "    \"\"\"\n",
    "    N = len(ics[0][1][3])\n",
    "    K = len(ics)\n",
    "    ic_i = np.zeros((N, K))\n",
    " \n",
    "    for i in range(K):\n",
    "        ic = ics[i][1][3]\n",
    "        if len(ic) != N:\n",
    "            raise ValueError('The number of observations should be the same '\n",
    "                             'across all models')\n",
    "        else:\n",
    "            ic_i[:, i] = ic\n",
    " \n",
    "    return N, K, ic_i\n",
    " \n",
    "def make_indices(dimensions):\n",
    "    # Generates complete set of indices for given dimensions\n",
    "    level = len(dimensions)\n",
    "    if level == 1:\n",
    "        return list(range(dimensions[0]))\n",
    "    indices = [[]]\n",
    "    while level:\n",
    "        _indices = []\n",
    "        for j in range(dimensions[level - 1]):\n",
    "            _indices += [[j] + i for i in indices]\n",
    "        indices = _indices\n",
    "        level -= 1\n",
    "    try:\n",
    "        return [tuple(i) for i in indices]\n",
    "    except TypeError:\n",
    "        return indices\n",
    " \n",
    " \n",
    "def calc_min_interval(x, alpha):\n",
    "    \"\"\"Internal method to determine the minimum interval of\n",
    "    a given width\n",
    " \n",
    "    Assumes that x is sorted numpy array.\n",
    "    \"\"\"\n",
    "    n = len(x)\n",
    "    cred_mass = 1.0 - alpha\n",
    " \n",
    "    interval_idx_inc = int(np.floor(cred_mass * n))\n",
    "    n_intervals = n - interval_idx_inc\n",
    "    interval_width = x[interval_idx_inc:] - x[:n_intervals]\n",
    " \n",
    "    if len(interval_width) == 0:\n",
    "        raise ValueError('Too few elements for interval calculation')\n",
    " \n",
    "    min_idx = np.argmin(interval_width)\n",
    "    hdi_min = x[min_idx]\n",
    "    hdi_max = x[min_idx + interval_idx_inc]\n",
    "    return hdi_min, hdi_max\n",
    " \n",
    " \n",
    "@statfunc\n",
    "def hpd(x, alpha=0.05, transform=lambda x: x):\n",
    "    \"\"\"Calculate highest posterior density (HPD) of array for given alpha. The HPD is the\n",
    "    minimum width Bayesian credible interval (BCI).\n",
    " \n",
    "    :Arguments:\n",
    "      x : Numpy array\n",
    "          An array containing MCMC samples\n",
    "      alpha : float\n",
    "          Desired probability of type I error (defaults to 0.05)\n",
    "      transform : callable\n",
    "          Function to transform data (defaults to identity)\n",
    " \n",
    "    \"\"\"\n",
    "    # Make a copy of trace\n",
    "    x = transform(x.copy())\n",
    " \n",
    "    # For multivariate node\n",
    "    if x.ndim > 1:\n",
    " \n",
    "        # Transpose first, then sort\n",
    "        tx = np.transpose(x, list(range(x.ndim))[1:] + [0])\n",
    "        dims = np.shape(tx)\n",
    " \n",
    "        # Container list for intervals\n",
    "        intervals = np.resize(0.0, dims[:-1] + (2,))\n",
    " \n",
    "        for index in make_indices(dims[:-1]):\n",
    " \n",
    "            try:\n",
    "                index = tuple(index)\n",
    "            except TypeError:\n",
    "                pass\n",
    " \n",
    "            # Sort trace\n",
    "            sx = np.sort(tx[index])\n",
    " \n",
    "            # Append to list\n",
    "            intervals[index] = calc_min_interval(sx, alpha)\n",
    " \n",
    "        # Transpose back before returning\n",
    "        return np.array(intervals)\n",
    " \n",
    "    else:\n",
    "        # Sort univariate node\n",
    "        sx = np.sort(x)\n",
    " \n",
    "        return np.array(calc_min_interval(sx, alpha))\n",
    " \n",
    "def _hpd_df(x, alpha):\n",
    "    cnames = ['hpd_{0:g}'.format(100 * alpha / 2),\n",
    "              'hpd_{0:g}'.format(100 * (1 - alpha / 2))]\n",
    "    return pd.DataFrame(hpd(x, alpha), columns=cnames)\n",
    " \n",
    " \n",
    "@statfunc\n",
    "def mc_error(x, batches=5):\n",
    "    R\"\"\"Calculates the simulation standard error, accounting for non-independent\n",
    "        samples. The trace is divided into batches, and the standard deviation of\n",
    "        the batch means is calculated.\n",
    " \n",
    "    Parameters\n",
    "    ----------\n",
    "    x : Numpy array\n",
    "              An array containing MCMC samples\n",
    "    batches : integer\n",
    "              Number of batches\n",
    " \n",
    "    Returns\n",
    "    -------\n",
    "    `float` representing the error\n",
    "    \"\"\"\n",
    "    if x.ndim > 1:\n",
    " \n",
    "        dims = np.shape(x)\n",
    "        #ttrace = np.transpose(np.reshape(trace, (dims[0], sum(dims[1:]))))\n",
    "        trace = np.transpose([t.ravel() for t in x])\n",
    " \n",
    "        return np.reshape([mc_error(t, batches) for t in trace], dims[1:])\n",
    " \n",
    "    else:\n",
    "        if batches == 1:\n",
    "            return np.std(x) / np.sqrt(len(x))\n",
    " \n",
    "        try:\n",
    "            batched_traces = np.resize(x, (batches, int(len(x) / batches)))\n",
    "        except ValueError:\n",
    "            # If batches do not divide evenly, trim excess samples\n",
    "            resid = len(x) % batches\n",
    "            new_shape = (batches, (len(x) - resid) / batches)\n",
    "            batched_traces = np.resize(x[:-resid], new_shape)\n",
    " \n",
    "        means = np.mean(batched_traces, 1)\n",
    " \n",
    "        return np.std(means) / np.sqrt(batches)\n",
    " \n",
    " \n",
    "@statfunc\n",
    "def quantiles(x, qlist=(2.5, 25, 50, 75, 97.5), transform=lambda x: x):\n",
    "    R\"\"\"Returns a dictionary of requested quantiles from array\n",
    " \n",
    "    Parameters\n",
    "    ----------\n",
    "    x : Numpy array\n",
    "        An array containing MCMC samples\n",
    "    qlist : tuple or list\n",
    "        A list of desired quantiles (defaults to (2.5, 25, 50, 75, 97.5))\n",
    "    transform : callable\n",
    "        Function to transform data (defaults to identity)\n",
    " \n",
    "    Returns\n",
    "    -------\n",
    "    `dictionary` with the quantiles {quantile: value}\n",
    "    \"\"\"\n",
    "    # Make a copy of trace\n",
    "    x = transform(x.copy())\n",
    " \n",
    "    # For multivariate node\n",
    "    if x.ndim > 1:\n",
    "        # Transpose first, then sort, then transpose back\n",
    "        sx = np.sort(x.T).T\n",
    "    else:\n",
    "        # Sort univariate node\n",
    "        sx = np.sort(x)\n",
    " \n",
    "    try:\n",
    "        # Generate specified quantiles\n",
    "        quants = [sx[int(len(sx) * q / 100.0)] for q in qlist]\n",
    " \n",
    "        return dict(zip(qlist, quants))\n",
    " \n",
    "    except IndexError:\n",
    "        pm._log.warning(\"Too few elements for quantile calculation\")\n",
    "def dict2pd(statdict, labelname):\n",
    "    \"\"\"Small helper function to transform a diagnostics output dict into a\n",
    "    pandas Series.\n",
    "    \"\"\"\n",
    "    from .backends import tracetab as ttab\n",
    "    var_dfs = []\n",
    "    for key, value in statdict.items():\n",
    "        var_df = pd.Series(value.flatten())\n",
    "        var_df.index = ttab.create_flat_names(key, value.shape)\n",
    "        var_dfs.append(var_df)\n",
    "    statpd = pd.concat(var_dfs, axis=0)\n",
    "    statpd = statpd.rename(labelname)\n",
    "    return statpd\n",
    " \n",
    "def summary(trace, varnames=None, transform=lambda x: x, stat_funcs=None,\n",
    "               extend=False, include_transformed=False,\n",
    "               alpha=0.05, start=0, batches=None):\n",
    "    R\"\"\"Create a data frame with summary statistics.\n",
    " \n",
    "    Parameters\n",
    "    ----------\n",
    "    trace : MultiTrace instance\n",
    "    varnames : list\n",
    "        Names of variables to include in summary\n",
    "    transform : callable\n",
    "        Function to transform data (defaults to identity)\n",
    "    stat_funcs : None or list\n",
    "        A list of functions used to calculate statistics. By default,\n",
    "        the mean, standard deviation, simulation standard error, and\n",
    "        highest posterior density intervals are included.\n",
    " \n",
    "        The functions will be given one argument, the samples for a\n",
    "        variable as a 2 dimensional array, where the first axis\n",
    "        corresponds to sampling iterations and the second axis\n",
    "        represents the flattened variable (e.g., x__0, x__1,...). Each\n",
    "        function should return either\n",
    " \n",
    "        1) A `pandas.Series` instance containing the result of\n",
    "           calculating the statistic along the first axis. The name\n",
    "           attribute will be taken as the name of the statistic.\n",
    "        2) A `pandas.DataFrame` where each column contains the\n",
    "           result of calculating the statistic along the first axis.\n",
    "           The column names will be taken as the names of the\n",
    "           statistics.\n",
    "    extend : boolean\n",
    "        If True, use the statistics returned by `stat_funcs` in\n",
    "        addition to, rather than in place of, the default statistics.\n",
    "        This is only meaningful when `stat_funcs` is not None.\n",
    "    include_transformed : bool\n",
    "        Flag for reporting automatically transformed variables in addition\n",
    "        to original variables (defaults to False).\n",
    "    alpha : float\n",
    "        The alpha level for generating posterior intervals. Defaults\n",
    "        to 0.05. This is only meaningful when `stat_funcs` is None.\n",
    "    start : int\n",
    "        The starting index from which to summarize (each) chain. Defaults\n",
    "        to zero.\n",
    "    batches : None or int\n",
    "        Batch size for calculating standard deviation for non-independent\n",
    "        samples. Defaults to the smaller of 100 or the number of samples.\n",
    "        This is only meaningful when `stat_funcs` is None.\n",
    " \n",
    "    See also\n",
    "    --------\n",
    "    summary : Generate a pretty-printed summary of a trace.\n",
    " \n",
    "    Returns\n",
    "    -------\n",
    "    `pandas.DataFrame` with summary statistics for each variable Defaults one\n",
    "    are: `mean`, `sd`, `mc_error`, `hpd_2.5`, `hpd_97.5`, `n_eff` and `Rhat`.\n",
    "    Last two are only computed for traces with 2 or more chains.\n",
    " \n",
    "    Examples\n",
    "    --------\n",
    "    .. code:: ipython\n",
    " \n",
    "        >>> import pymc3 as pm\n",
    "        >>> trace.mu.shape\n",
    "        (1000, 2)\n",
    "        >>> pm.summary(trace, ['mu'])\n",
    "                   mean        sd  mc_error     hpd_5    hpd_95\n",
    "        mu__0  0.106897  0.066473  0.001818 -0.020612  0.231626\n",
    "        mu__1 -0.046597  0.067513  0.002048 -0.174753  0.081924\n",
    " \n",
    "                  n_eff      Rhat\n",
    "        mu__0     487.0   1.00001\n",
    "        mu__1     379.0   1.00203\n",
    " \n",
    "    Other statistics can be calculated by passing a list of functions.\n",
    " \n",
    "    .. code:: ipython\n",
    " \n",
    "        >>> import pandas as pd\n",
    "        >>> def trace_sd(x):\n",
    "        ...     return pd.Series(np.std(x, 0), name='sd')\n",
    "        ...\n",
    "        >>> def trace_quantiles(x):\n",
    "        ...     return pd.DataFrame(pm.quantiles(x, [5, 50, 95]))\n",
    "        ...\n",
    "        >>> pm.summary(trace, ['mu'], stat_funcs=[trace_sd, trace_quantiles])\n",
    "                     sd         5        50        95\n",
    "        mu__0  0.066473  0.000312  0.105039  0.214242\n",
    "        mu__1  0.067513 -0.159097 -0.045637  0.062912\n",
    "    \"\"\"\n",
    "    from .backends import tracetab as ttab\n",
    " \n",
    "    if varnames is None:\n",
    "        varnames = get_default_varnames(trace.varnames,\n",
    "                       include_transformed=include_transformed)\n",
    " \n",
    "    if batches is None:\n",
    "        batches = min([100, len(trace)])\n",
    " \n",
    "    funcs = [lambda x: pd.Series(np.mean(x, 0), name='mean'),\n",
    "             lambda x: pd.Series(np.std(x, 0), name='sd'),\n",
    "             lambda x: pd.Series(mc_error(x, batches), name='mc_error'),\n",
    "             lambda x: _hpd_df(x, alpha)]\n",
    " \n",
    "    if stat_funcs is not None:\n",
    "        if extend:\n",
    "            funcs = funcs + stat_funcs\n",
    "        else:\n",
    "            funcs = stat_funcs\n",
    " \n",
    "    var_dfs = []\n",
    "    for var in varnames:\n",
    "        vals = transform(trace.get_values(var, burn=start, combine=True))\n",
    "        flat_vals = vals.reshape(vals.shape[0], -1)\n",
    "        var_df = pd.concat([f(flat_vals) for f in funcs], axis=1)\n",
    "        var_df.index = ttab.create_flat_names(var, vals.shape[1:])\n",
    "        var_dfs.append(var_df)\n",
    "    dforg = pd.concat(var_dfs, axis=0)\n",
    " \n",
    "    if (stat_funcs is not None) and (not extend):\n",
    "        return dforg\n",
    "    elif trace.nchains < 2:\n",
    "        return dforg\n",
    "    else:\n",
    "        n_eff = pm.effective_n(trace,\n",
    "                               varnames=varnames,\n",
    "                               include_transformed=include_transformed)\n",
    "        n_eff_pd = dict2pd(n_eff, 'n_eff')\n",
    "        rhat = pm.gelman_rubin(trace,\n",
    "                               varnames=varnames,\n",
    "                               include_transformed=include_transformed)\n",
    "        rhat_pd = dict2pd(rhat, 'Rhat')\n",
    "        return pd.concat([dforg, n_eff_pd, rhat_pd],\n",
    "                         axis=1, join_axes=[dforg.index])\n",
    " \n",
    " \n",
    "def df_summary(*args, **kwargs):\n",
    "    warnings.warn(\"df_summary has been deprecated. In future, use summary instead.\",\n",
    "                  DeprecationWarning, stacklevel=2)\n",
    "    return summary(*args, **kwargs)\n",
    " \n",
    "def _calculate_stats(sample, batches, alpha):\n",
    "    means = sample.mean(0)\n",
    "    sds = sample.std(0)\n",
    "    mces = mc_error(sample, batches)\n",
    "    intervals = hpd(sample, alpha)\n",
    "    for key, idxs in _groupby_leading_idxs(sample.shape[1:]):\n",
    "        yield key\n",
    "        for idx in idxs:\n",
    "            mean, sd, mce = [stat[idx] for stat in (means, sds, mces)]\n",
    "            interval = intervals[idx].squeeze().tolist()\n",
    "            yield {'mean': mean, 'sd': sd, 'mce': mce, 'hpd': interval}\n",
    " \n",
    " \n",
    "def _calculate_posterior_quantiles(sample, qlist):\n",
    "    var_quantiles = quantiles(sample, qlist=qlist)\n",
    "    # Replace ends of qlist with 'lo' and 'hi'\n",
    "    qends = {qlist[0]: 'lo', qlist[-1]: 'hi'}\n",
    "    qkeys = {q: qends[q] if q in qends else 'q{}'.format(q) for q in qlist}\n",
    "    for key, idxs in _groupby_leading_idxs(sample.shape[1:]):\n",
    "        yield key\n",
    "        for idx in idxs:\n",
    "            yield {qkeys[q]: var_quantiles[q][idx] for q in qlist}\n",
    " \n",
    " \n",
    "def _groupby_leading_idxs(shape):\n",
    "    \"\"\"Group the indices for `shape` by the leading indices of `shape`.\n",
    " \n",
    "    All dimensions except for the rightmost dimension are used to create\n",
    "    groups.\n",
    " \n",
    "    A 3d shape will be grouped by the indices for the two leading\n",
    "    dimensions.\n",
    " \n",
    "        >>> for key, idxs in _groupby_leading_idxs((3, 2, 2)):\n",
    "        ...     print('key: {}'.format(key))\n",
    "        ...     print(list(idxs))\n",
    "        key: (0, 0)\n",
    "        [(0, 0, 0), (0, 0, 1)]\n",
    "        key: (0, 1)\n",
    "        [(0, 1, 0), (0, 1, 1)]\n",
    "        key: (1, 0)\n",
    "        [(1, 0, 0), (1, 0, 1)]\n",
    "        key: (1, 1)\n",
    "        [(1, 1, 0), (1, 1, 1)]\n",
    "        key: (2, 0)\n",
    "        [(2, 0, 0), (2, 0, 1)]\n",
    "        key: (2, 1)\n",
    "        [(2, 1, 0), (2, 1, 1)]\n",
    " \n",
    "    A 1d shape will only have one group.\n",
    " \n",
    "        >>> for key, idxs in _groupby_leading_idxs((2,)):\n",
    "        ...     print('key: {}'.format(key))\n",
    "        ...     print(list(idxs))\n",
    "        key: ()\n",
    "        [(0,), (1,)]\n",
    "    \"\"\"\n",
    "    idxs = itertools.product(*[range(s) for s in shape])\n",
    "    return itertools.groupby(idxs, lambda x: x[:-1])\n",
    " \n",
    "def bfmi(trace):\n",
    "    R\"\"\"Calculate the estimated Bayesian fraction of missing information (BFMI).\n",
    " \n",
    "    BFMI quantifies how well momentum resampling matches the marginal energy\n",
    "    distribution.  For more information on BFMI, see\n",
    "    https://arxiv.org/pdf/1604.00695.pdf.  The current advice is that values\n",
    "    smaller than 0.2 indicate poor sampling.  However, this threshold is\n",
    "    provisional and may change.  See\n",
    "    http://mc-stan.org/users/documentation/case-studies/pystan_workflow.html\n",
    "    for more information.\n",
    " \n",
    "    Parameters\n",
    "    ----------\n",
    "    trace : result of an HMC/NUTS run, must contain energy information\n",
    " \n",
    "    Returns\n",
    "    -------\n",
    "    z : float\n",
    "        The Bayesian fraction of missing information of the model and trace.\n",
    "    \"\"\"\n",
    "    energy = trace['energy']\n",
    " \n",
    "    return np.square(np.diff(energy)).mean() / np.var(energy)\n",
    " \n",
    "def r2_score(y_true, y_pred, round_to=2):\n",
    "    R\"\"\"R-squared for Bayesian regression models. Only valid for linear models.\n",
    "    http://www.stat.columbia.edu/%7Egelman/research/unpublished/bayes_R2.pdf\n",
    " \n",
    "    Parameters\n",
    "    ----------\n",
    "    y_true: : array-like of shape = (n_samples) or (n_samples, n_outputs)\n",
    "        Ground truth (correct) target values.\n",
    "    y_pred : array-like of shape = (n_samples) or (n_samples, n_outputs)\n",
    "        Estimated target values.\n",
    "    round_to : int\n",
    "        Number of decimals used to round results (default 2).\n",
    " \n",
    "    Returns\n",
    "    -------\n",
    "    `namedtuple` with the following elements:\n",
    "    R2_median: median of the Bayesian R2\n",
    "    R2_mean: mean of the Bayesian R2\n",
    "    R2_std: standard deviation of the Bayesian R2\n",
    "    \"\"\"\n",
    "    dimension = None\n",
    "    if y_true.ndim > 1:\n",
    "        dimension = 1\n",
    " \n",
    "    var_y_est = np.var(y_pred, axis=dimension)\n",
    "    var_e = np.var(y_true - y_pred, axis=dimension)\n",
    " \n",
    "    r2 = var_y_est / (var_y_est + var_e)\n",
    "    r2_median = np.around(np.median(r2), round_to)\n",
    "    r2_mean = np.around(np.mean(r2), round_to)\n",
    "    r2_std = np.around(np.std(r2), round_to)\n",
    "    r2_r = namedtuple('r2_r', 'r2_median, r2_mean, r2_std')\n",
    "    return r2_r(r2_median, r2_mean, r2_std)\n",
    " "
   ]
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   "source": []
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